Near-earth spacecraft strong transverse maneuvering reentry trajectory planning method

Abstract

The invention relates to a near-earth spacecraft strong transverse maneuvering reentry trajectory planning method. The method comprises the following steps: determining basic parameters of return reentry trajectory planning; calculating a reentry trajectory of the maneuver without transverse offset; distributing a transverse maneuver amount, and establishing a transverse maneuver planning equation; calculating a braking yaw angle; calculating an initial value of the heeling angle offset; establishing a funnel guidance law under the condition of transverse offset maneuvering; according to the determined return and reentry trajectory planning basic parameters, the total transverse offset maneuver amount, the braking yaw angle and the funnel guidance law under the transverse offset maneuver condition, the initial value of the heeling angle offset amount, the time of the braking point relative to the return circle ascending node and the braking starting duration serve as initial values, reentry trajectory parameters are iteratively solved, and reentry trajectory planning is completed. According to the method, the problem of rapid planning of the reentry trajectory when the ground proximity device returns to the designated position under the condition of large initial transverse deviation is solved, and meanwhile, the problem of rapid planning of the reentry trajectory when the landing point needs to avoid the designated area can be solved.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of reentry trajectory planning of near-earth spacecraft, and relates to a strong lateral maneuvering reentry trajectory planning method of near-earth spacecraft. BACKGROUND

[0002] Return refers to the process that a spacecraft enters the earth's atmosphere along its operating orbit or a transition orbit after orbit transfer, and is decelerated and lands under the action of aerodynamic force. The operating trajectory of the spacecraft in the return process is called a return orbit. The return orbit of a near-earth spacecraft can be divided into a posture adjusting segment, a braking segment, a sliding segment, a reentry segment and a landing segment, and different dynamic models are used in each segment, and the calculation process is relatively complex. In the return process of the spacecraft, high-speed reentry results in serious aerodynamic heating and a harsh environment, and the deceleration overload in the reentry process, the heat flux and total heat absorption caused by aerodynamic heating and landing accuracy are all constraint conditions for the design of the return orbit. Therefore, the design of the return orbit generally adopts an iterative process, and a nominal return orbit satisfying the constraint conditions is obtained through iterative calculation, overall optimization is realized, parameters are provided for the design of a heat protection system, a structure design, a control system design and a propulsion system design, and information is provided for a measurement and control system and a recovery system.

[0003] The existing return spacecraft generally has a small lift-drag ratio, which is generally less than 0.5, and the size of the trim angle of attack is limited by the lateral displacement of the center of mass and cannot be too large. The lift used and the drag used will not exceed 0.5 (Aircraft Reentry Dynamics and Guidance, Zhao Han-yuan, National Defense Science and Technology University Press, P340). For the return of a small lift-drag ratio spacecraft, the control quantity is the roll angle, and the size and sign of the roll angle are controlled according to a certain control logic in the reentry process of the spacecraft, so as to change the components of the lift in the local vertical plane and the horizontal plane, thereby controlling the landing position and the reentry overload of the return within a certain range. Since the control quantity is only the roll angle, but the deviation quantity is the heading deviation and the lateral deviation, the heading deviation control is usually achieved by changing the size of the roll angle to adjust the component of the lift in the horizontal plane, and the change of the sign of the roll angle is controlled by using a lateral funnel (Aircraft Reentry Dynamics and Guidance, Zhao Han-yuan, National Defense Science and Technology University Press, P347) to realize the positive and negative alternation and gradual reduction of the lateral deviation. In the above reentry guidance method, the size change of the roll angle is achieved through the feedback control of the heading deviation, and the control demand of the lateral deviation cannot be considered. The control of the lateral deviation can only rely on the lateral funnel. Therefore, in the reentry process of the small lift-drag ratio spacecraft, the lateral maneuvering capability is weak, and the lateral deviation elimination within a small range can usually be achieved. SUMMARY

[0004] The technical problem solved by the present application is to overcome the shortcomings of the prior art and provide a near-earth spacecraft strong lateral maneuver reentry trajectory planning method, which solves the problem of rapid planning of a reentry trajectory of a near-earth spacecraft returning to a specified position under a large initial lateral deviation, and can also solve the problem of rapid planning of a reentry trajectory of a near-earth spacecraft avoiding a specified area.

[0005] The technical problem solved by the present application is a near-earth spacecraft strong lateral maneuver reentry trajectory planning method, comprising the following steps:

[0006] S1, determining basic parameters of return reentry trajectory planning, including an orbit inclination i0, a longitude λ of an expected return aiming point D and a geocentric latitude a target reentry angle θ e , initial and terminal values obtained by linear segmentation of a reentry segment inclination angle, a lateral guidance coefficient, and a braking pitch angle a propellant consumption ΔM allowed by braking;

[0007] S2, determining a point C with the same longitude as the expected return aiming point on a sub-satellite point trajectory as a return aiming point without lateral deviation maneuvering according to orbit elements of a return orbit, calculating a return reentry trajectory without lateral deviation maneuvering by using the basic parameters of return reentry trajectory planning in step S1, and outputting a time t of a braking point relative to a return orbit ascending node b , a braking start time t p , a braking point longitude λ B and a geocentric latitude a reentry point longitude λ R and a geocentric latitude a lateral deviation maneuvering amount Z of yaw braking B , a propellant consumption Δm;

[0008] S3, calculating a lateral deviation maneuvering amount Z of yaw braking according to a linear relationship between a propellant consumption and a lateral deviation and a lateral braking speed increment corresponding to a propellant consumption of a reentry segment, determining a reentry segment lateral deviation maneuvering amount Z 0b , and determining a total lateral deviation maneuvering amount Z0 as a sum of the lateral deviation maneuvering amount Z 0r of yaw braking and the reentry segment lateral deviation maneuvering amount Z 0b . 0r

[0009] S4, calculating a yaw braking angle ψ by using spherical trigonometry, a relationship between an orbit inclination change and a lateral speed increment according to the return reentry trajectory parameters without lateral deviation maneuvering output in step S2.

[0010] ​S5, based on the return reentry trajectory without lateral bias maneuvering of step S2, biasing the roll angle sequence, calculating the corresponding aiming point lateral deviation, determining the initial value of the roll angle biasing amount according to the linear relationship between the roll angle sequence lateral biasing amount and the aiming point lateral deviation and the reentry segment lateral biasing maneuvering amount Z 0r ;

[0011] S6, establishing the reentry coordinate system according to the reentry point longitude λ R , the reentry point geocentric latitude and the return aiming point C without lateral bias maneuvering, transforming the lateral range, and adding the reentry segment lateral biasing maneuvering amount Z 0r to the funnel boundary of the non-bias funnel guidance law to establish the funnel guidance law under the condition of lateral bias maneuvering;

[0012] S7, according to the return reentry trajectory planning basic parameters determined in step S1, the total lateral bias maneuvering amount Z0 determined in step S3, the yaw angle ψ determined in step S4, the funnel guidance law under the condition of lateral bias maneuvering determined in step S6, taking the initial value of the roll angle biasing amount of step S5, the time t b of the braking point relative to the ascending node of the return orbit, the braking on time t p as the initial value, iteratively solving the reentry trajectory parameters to complete the reentry trajectory planning.

[0013] Further, the calculation of the return reentry trajectory without lateral bias maneuvering comprises:

[0014] the braking on time t p , taking the target reentry angle θ e as the iterative target, and iteratively solving by using the numerical difference gradient or the sequential quadratic programming algorithm; the time t b of the braking point relative to the ascending node of the return orbit, taking the total range from the braking point to the return aiming point C without lateral bias maneuvering as the iterative target, and iteratively solving by using the numerical difference gradient or the sequential quadratic programming algorithm. In the iterative process, if t b > 0, extrapolating the orbit from the ascending node orbit of the return orbit, and if t b < 0, backtracking the orbit from the ascending node orbit of the return orbit;

[0015] When the reentry angle deviation is less than the allowable deviation and the total range deviation is less than the allowable deviation, the iterative calculation is stopped, the reentry trajectory parameters are output, and the finally obtained time t b of the braking point relative to the ascending node of the return orbit, the braking on time t p , the braking point longitude λ B and the geocentric latitude are recorded. R The braking speed increment Δv without lateral bias maneuvering​B , the propellant consumption Δm, the latitude amplitude u0 of the braking point.

[0016] Further, the reentry course guidance adopts a gradually decreasing bank angle sequence, and the lateral guidance adopts a funnel guidance law without bias.

[0017] Further, the lateral bias maneuver Z 0b is calculated by:

[0018] Z 0b = (ΔM-Δm) δZ 0b / δΔm

[0019] δZ 0b is the lateral deviation at the end of the reentry segment, and δΔm is the increased braking propellant consumption.

[0020] Further, the lateral bias maneuver Z 0r is calculated by:

[0021] Let the coefficient 0 < c e < 1, and the maximum bank angle bias be c e [90-max(γ′ 1s , γ′ 1e )], where γ′ 1s and γ′ 1e are the initial value and the terminal value of the first segment of the straight line of the bank angle, respectively; based on the maximum bank angle bias and the calculation result of the reentry trajectory without lateral bias maneuver, the maximum lateral bias maneuver Z' 0r is obtained through numerical calculation, and according to actual needs, the lateral bias maneuver Z 0r is determined within the range of Z' 0r .

[0022] Further, the braking yaw angle ψ is calculated by:

[0023] 401. The arc lengths of the three sides of the spherical triangle BCD are calculated, where point B is the braking point, point C is the return aiming point without lateral bias maneuver, and point D is the desired return aiming point;

[0024] The arc length d of the circular arc BC in radians is:

[0025]

[0026] The arc length b of the circular arc CD in radians is:

[0027]

[0028] The arc length c of the circular arc BD in radians is:

[0029]

[0030] where λB and φB are the longitude and geocentric latitude of the braking point B, respectively, λC and φC are the longitude and geocentric latitude of the return aiming point C without lateral bias maneuver, respectively, and λD and φD are the longitude and geocentric latitude of the desired return aiming point D, respectively. B and where λB and φB are the longitude and geocentric latitude of the braking point B, respectively, λC and φC are the longitude and geocentric latitude of the return aiming point C without lateral bias maneuver, respectively, and λD and φD are the longitude and geocentric latitude of the desired return aiming point D, respectively. C and where λB and φB are the longitude and geocentric latitude of the braking point B, respectively, λC and φC are the longitude and geocentric latitude of the return aiming point C without lateral bias maneuver, respectively, and λD and φD are the longitude and geocentric latitude of the desired return aiming point D, respectively. D and where λB and φB are the longitude and geocentric latitude of the braking point B, respectively, λC and φC are the longitude and geocentric latitude of the return aiming point C without lateral bias maneuver, respectively, and λD and φD are the longitude and geocentric latitude of the desired return aiming point D, respectively.

[0031] 402, calculate the track yaw angle Δσ:

[0032]

[0033] 403, calculate the orbit inclination i after the yaw braking:

[0034] i = arccos (cos Δσ cos i0- sin Δσ sin i0cos u0) i0is the orbit inclination at the epoch T0of the ascending node of the return orbit, and u0is the latitude amplitude angle of the braking point.

[0035] 404, calculate the normal velocity increment Δv h :

[0036]

[0037] μ, p, r are the earth gravity constant, the semi-orthogonal chord of the orbit before braking, and the geocentric distance of the braking point, respectively.

[0038] 405, calculate the braking yaw angle ψ:

[0039]

[0040] Δv B is the braking velocity increment without lateral bias maneuver, is the braking pitch angle, and arctan2 (y, x) is the inverse tangent function for determining the angle quadrant according to the input y, x.

[0041] Further, the initial value of the roll angle bias is determined by the method:

[0042] On the basis of the calculation result of the reentry trajectory without lateral bias maneuver, the roll angle sequence is increased by the bias δγ0, and the return reentry trajectory is calculated again to obtain the lateral deviation δZ 0r at the terminal of the reentry segment, and then the initial value γ0of the roll angle bias is:

[0043] γ0= Z 0r δγ0 / δZ 0r .

[0044] Further, the funnel guidance law in the case of lateral bias maneuver is established by the method of:

[0045] According to the longitude of reentry point λ R , the geocentric latitude of reentry point and the return aiming point C without lateral bias maneuver, the reentry coordinate system is established, and the inclination angle before bias is γ' c and the inclination angle after bias is γ c , then:

[0046] γ c = γ' c + γ0

[0047] In order to control the lateral deviation with the total lateral bias maneuver Z0as the target, the lateral distance Z' in the reentry coordinate system is transformed:

[0048] Z' = Z + Z 0r

[0049] Z is the lateral distance in the reentry coordinate system without considering the lateral maneuver;

[0050] The funnel guidance law in the case of lateral bias maneuver is as follows:

[0051]

[0052]

[0053] K5 = C z3 + C z4 (v / v e )

[0054] Where v is the speed relative to the earth, v e is the reentry speed, is the derivative of Z', is the funnel boundary, K5 is the coefficient, γ is the inclination angle at the current time, γ(k-1) is the inclination angle at the last time, C z1 , C z2 , C z3 , C z4 are lateral guidance coefficients; when the inclination angle changes sign, the inclination angle size is:

[0055]

[0056] Where Δt is the control period, is the angular velocity of the inclination angle flip, γ is is the starting inclination angle after the sign change after bias.

[0057] Further, the step S7 adopts a numerical difference gradient iteration or a sequential quadratic programming algorithm to iteratively solve the reentry trajectory parameters.

[0058] Further, the iteratively solving the reentry trajectory parameters comprises:

[0059] taking the target reentry angle θ e as the iteration target to iteratively solve the braking start time t p , taking the total distance from the braking point to the expected return aiming point as the iteration target to iteratively solve the time t of the braking point relative to the ascending node of the return orbit, b taking the total lateral bias maneuver Z0 as the iteration target to iteratively solve the roll angle bias, adopting a numerical difference calculation gradient matrix and a gradient iteration algorithm to complete the solving;

[0060] or, taking the braking start time t p , the time t of the braking point relative to the ascending node of the return orbit, b and the roll angle bias as optimization variables, taking the reentry angle θ e as the equality constraint, taking the sum of squares of the longitude deviation and the geocentric latitude deviation of the return trajectory terminal and the expected return aiming point as the optimization target, and adopting a sequential quadratic programming algorithm to complete the iterative solving.

[0061] Compared with the prior art, the present application has the following beneficial effects:

[0062] (1) The present application distributes the lateral maneuver according to the lateral bias maneuver generated by the yaw braking and the lateral bias maneuver in the reentry section, calculates the braking yaw angle according to the spherical triangle geometry relationship, the relationship between the orbit inclination change and the lateral velocity increment, determines the initial value of the roll angle bias according to the linear relationship between the roll angle sequence lateral bias and the lateral deviation of the aiming point and the lateral bias maneuver generated by the roll angle bias, establishes the funnel guidance law under the lateral bias maneuver condition, finally takes the reentry angle as the target to iteratively solve the braking velocity increment, takes the distance as the target to iteratively solve the braking start time, and takes the total lateral bias maneuver as the iteration target to complete the iterative solving of the roll angle bias. This method can solve the rapid planning of the reentry trajectory for the lateral adjustment of the aiming point and the regional avoidance of the manned spacecraft during the return of the manned spacecraft, and has been applied to the rapid planning of the nominal reentry trajectory of the rapid return of the manned spacecraft. BRIEF DESCRIPTION OF DRAWINGS

[0063] Figure 1 The figure is a flow chart of the reentry trajectory planning method of the near-earth spacecraft according to the present application;

[0064] Figure 2 The figure is a spacecraft return schematic diagram according to the embodiment of the present application;

[0065] Figure 3A schematic diagram of lateral maneuvering quantity distribution for the embodiment of the present application;

[0066] Figure 4 A spherical geometry relationship for solving the yaw angle of the flight path for the embodiment of the present application;

[0067] Figure 5 A sequence of the bank angle after biasing for the embodiment of the present application;

[0068] Figure 6 A lateral funnel and lateral deviation after biasing for the embodiment of the present application. DETAILED DESCRIPTION

[0069] For the given initial condition of the return front orbit, a yaw braking strategy and a control time curve of the bank angle in the reentry section can be found in the reentry corridor, which makes the manned spacecraft return capsule have the desired trajectory condition at the terminal of the reentry section under the constraints of the braking propellant and the overload in the return reentry process, so as to meet the longitude and latitude requirements of the parachute opening point, and facilitate the return capsule to be recovered and landed at the predetermined landing site.

[0070] The present application provides a reentry trajectory planning method for realizing strong lateral maneuvering of a near-earth spacecraft, proposes a strong lateral maneuvering quantity realization method combined by braking yaw and bank angle biasing, provides a calculation method of the braking yaw angle, an initial value and a final solution of the lateral biasing quantity of the bank angle, and clarifies the funnel guidance law under the condition of lateral biasing maneuvering, and provides a solving step.

[0071] The present application will be further described below in combination with the drawings and embodiments.

[0072] The near-earth spacecraft strong lateral maneuvering reentry trajectory planning method of the present application comprises the following steps:

[0073] S1, determining the basic parameters of the return reentry trajectory planning, including the orbit inclination i0, the longitude λ of the desired return aiming point D and the geocentric latitude the target reentry angle θ e , the initial value and the terminal value obtained by linearly segmenting the bank angle in the reentry section, the lateral guidance coefficient, and the braking pitch angle the propellant consumption ΔM allowed by braking;

[0074] S2, determining the point C with the same longitude as the desired return aiming point on the sub-satellite point trajectory as the return aiming point without lateral biasing maneuvering according to the orbital elements of the return orbit, calculating the return reentry trajectory without lateral biasing maneuvering by using the basic parameters of the return reentry trajectory planning in step S1, and outputting the time t of the braking point relative to the ascending node of the return orbit b , the braking on-time t p , the braking point longitude λ B and the geocentric latitude Reentry point longitude λ R and geocentric latitude Braking velocity increment Δv without lateral bias maneuver B , propellant consumption Δm; the reentry process heading guidance adopts a gradually decreasing bank angle sequence, and the lateral guidance adopts a funnel guidance law without bias;

[0075] S3, calculating the lateral bias maneuver Z generated by yaw braking according to the linear relationship between the propellant consumption Δm, the allowed propellant consumption ΔM of braking, and the propellant consumption corresponding to the lateral deviation and lateral braking velocity increment of the reentry segment 0b , calculating the maximum value of the lateral bias maneuver of the reentry segment generated by the bank angle bias, and determining the lateral bias maneuver Z of the reentry segment within the range of the maximum value 0r , the total lateral bias maneuver Z0 is the sum of the lateral bias maneuver Z generated by yaw braking and the lateral bias maneuver of the reentry segment generated by the bank angle bias 0b ; 0r

[0076] S4, calculating the braking yaw angle ψ according to the return reentry trajectory parameters without lateral bias maneuver output in step S2, using spherical trigonometry, the relationship between the change of orbit inclination and the lateral velocity increment

[0077] S5, based on the return reentry trajectory without lateral bias maneuver calculated in step S2, biasing the bank angle sequence, calculating the corresponding lateral deviation of the aiming point, and determining the initial value of the bank angle biasing amount according to the linear relationship between the lateral biasing amount of the bank angle sequence and the lateral deviation of the aiming point and the lateral bias maneuver Z of the reentry segment 0r ;

[0078] S6, establishing the reentry coordinate system according to the reentry point longitude λ R , the reentry point geocentric latitude and the return aiming point C without lateral bias maneuver, transforming the cross-range in the reentry coordinate system, and increasing the lateral bias maneuver Z of the reentry segment on the basis of the funnel boundary of the funnel guidance law without bias to establish the funnel guidance law under the condition of lateral bias maneuver 0r ;

[0079] S7, according to the return reentry trajectory planning basic parameters determined in step S1, the total lateral bias maneuver Z0 determined in step S3, the braking yaw angle ψ determined in step S4, and the funnel guidance law under the condition of lateral bias maneuver determined in step S6, taking the initial value of the bank angle biasing amount in step S5 and the time t b of the braking point relative to the ascending node of the return orbit in step S2 and the braking on time t p as the initial value, and solving the reentry trajectory parameters by using the gradient iteration or sequence quadratic programming iteration algorithm, including the reentry point longitude λ​B and geocentric latitude braking speed increment Δv B , roll angle offset, complete the reentry trajectory planning.

[0080] Embodiment 1

[0081] As Figure 1 , the near-earth spacecraft strong lateral maneuver reentry trajectory planning method of the embodiment has the following steps:

[0082] S1, determine the basic parameters of the return reentry trajectory planning.

[0083] Let the orbital semi-major axis of the ascending node of the return circle at the epoch time T0 be a0, the eccentricity be e0, the orbital inclination be i0, the ascending node right ascension be Ω0, the perigee amplitude be ω0, the true anomaly be θ0, the longitude of the desired return aiming point be λ D , the geocentric latitude be the target reentry angle be θ e , the lateral guidance coefficient be C z1 , C z2 , C z3 , C z4 , the braking pitch angle be the braking allowed propellant consumption ΔM; the roll angle is segmented according to straight lines for the reentry segment, the starting value and the terminal value of the first segment of the segmented straight line of the roll angle are γ′ 1s , γ′ 1e , the starting value and the terminal value of the second segment of the segmented straight line are γ' 2s , γ' 2e , the starting value and the terminal value of the third segment of the segmented straight line are γ' 3s , γ' 3e , the starting value and the terminal value of the fourth segment of the segmented straight line are γ' 4s , γ' 4e , the starting value and the terminal value of the nth segment of the segmented straight line are γ' ns , γ' ne , the slope of the segmented straight line can be set as needed, and in general cases, the slope can be set to 0.

[0084] S2, calculate the reentry trajectory without lateral offset maneuver.

[0085] Let the time of the braking point relative to the ascending node of the return circle be t b , t b > 0, the braking start time is after the ascending node of the return circle, t b < 0, the braking start time is before the ascending node of the return circle, and the braking initial duration is t p0 .

[0086] The braking start duration tp with the target reentry angle θ e is solved by numerical difference gradient iteration; the time t b of the braking point relative to the ascending node of the return orbit is solved by numerical difference gradient iteration with the total range from the braking point to the return aiming point C without lateral bias maneuver as the iteration target. In the iteration process, if t b > 0, the orbit is extrapolated from the ascending node of the return orbit, and if t b < 0, the orbit is extrapolated from the descending node of the return orbit. The calculation process considers the J2 term perturbation, and higher order gravity perturbation can be considered according to the calculation accuracy requirement. The spacecraft return schematic diagram is shown in Figure 2 .

[0087] When the reentry angle deviation is less than the allowable deviation and the total range deviation is less than the allowable deviation, the iteration calculation is stopped, and the reentry trajectory parameters are output, and the finally obtained braking point relative to the ascending node of the return orbit time t b , braking start time t p , braking point longitude λ B and geocentric latitude reentry point longitude λ R and geocentric latitude lateral bias maneuver braking speed increment Δv B , propellant consumption Δm, and latitude amplitude u0 of the braking point are recorded.

[0088] The above iteration calculation process can also be completed by using other programming algorithms such as sequential quadratic programming in addition to numerical difference gradient iteration.

[0089] In the above iteration calculation process, the heading guidance in the reentry process adopts a gradually decreasing bank angle sequence, and the lateral guidance adopts a funnel guidance law without bias.

[0090] S3, distribute the lateral maneuver amount and establish a lateral maneuver programming equation.

[0091] Distribute the lateral maneuver amount and establish a lateral maneuver programming equation according to the following 3 sub-steps:

[0092] 301, calculate the relationship between the lateral braking speed increment and the lateral bias maneuver amount, and determine the lateral bias maneuver amount generated by yaw braking. On the basis of the calculation result of the return reentry trajectory without lateral bias maneuver, the lateral braking speed increment δΔv h is added, the return reentry trajectory is calculated again, the lateral deviation δZ 0b at the end of the reentry section is obtained, and the added braking propellant consumption is δΔm.

[0093] The lateral bias maneuver amount Z 0b generated by yaw braking is:

[0094] Z0b = (ΔM - Δm) δZ 0b / δΔm (1)

[0095] 302, calculate the maximum value of the reentry lateral bias maneuver Z produced by the roll angle bias, determine the reasonable reentry lateral bias maneuver Z 0r .

[0096] Let the coefficient 0 < c e < 1, c e According to the reasonable selection of the lateral deviation control ability under the condition of no lateral bias maneuver, the maximum roll angle bias is c e [90 - max (γ' 1s , γ' 1e )], based on the calculation results of the maximum roll angle bias and the reentry trajectory without lateral bias maneuver, the maximum reentry lateral bias maneuver Z' 0r is obtained by numerical calculation. According to the actual needs, the reasonable reentry lateral bias maneuver Z 0r is determined within the range of Z' 0r .

[0097] 303, as Figure 3 , establish the lateral maneuver planning equation, and the total lateral bias maneuver Z0 is:

[0098] Z0 = Z 0b + Z 0r (2)S4, calculate the brake yaw angle ψ.

[0099] As Figure 4 , the calculation of the brake yaw angle ψ is divided into the following 5 sub-steps:

[0100] 401, calculate the arc length of the spherical triangle BCD, where point B is the braking point, point C is the return aiming point without lateral bias maneuver, and point D is the expected return aiming point;

[0101] The arc length d of the circular arc BC in radian is:

[0102]

[0103] The arc length b of the circular arc CD in radian is:

[0104]

[0105] The arc length c of the circular arc BD in radian is:

[0106]

[0107] Where, λ B and respectively the longitude and geocentric latitude of the braking point B, λ C and respectively the longitude and geocentric latitude of the return aiming point C without lateral bias maneuver, λ D and respectively the longitude and geocentric latitude of the desired return aiming point D;

[0108] 402, calculate the track yaw angle Δσ

[0109]

[0110] 403, calculate the track inclination i after yaw braking

[0111] i = arccos (cos Δσ cos i0- sin Δσ sin i0cos u0) (7) i0is the track inclination of the return circle ascending node at the epoch time T0, u0is the latitude amplitude angle of the braking point;

[0112] 404, calculate the normal velocity increment Δv h

[0113]

[0114] μ, p, r are respectively the earth gravity constant, the semi-orthogonal chord of the orbit before braking, and the geocentric distance of the braking point;

[0115] 405, calculate the braking yaw angle ψ

[0116]

[0117] Δv B is the braking velocity increment without lateral bias maneuver, is the braking pitch angle, arctan2 (y, x) is the inverse tangent function for determining the angle quadrant according to the input y, x.

[0118] S5, calculate the initial value of the roll angle bias amount.

[0119] On the basis of the calculation results of the reentry trajectory without lateral bias maneuver, the roll angle sequence is increased by the bias amount δγ0, the return reentry trajectory is calculated again, and the lateral deviation δZ of the reentry segment terminal is obtained 0r Then the initial value γ0 of the roll angle bias amount is:

[0120] γ0= Z 0r δγ0 / δZ 0r (10)

[0121] S6, establish the funnel guidance law under the condition of lateral bias maneuver.

[0122] According to the reentry point longitude λR Reentry point geocentric latitude Establish a reentry coordinate system with the return aiming point C without lateral offset maneuvering. When calculating the yaw braking reentry trajectory, the lateral effect of yaw braking on the flight trajectory occurs after braking; the lateral maneuver during reentry needs to be generated through offset roll angle during the reentry flight. Let the roll angle before offset be γ'. c The tilt angle after offset is γ c ,like Figure 5 The relationship between the tilt angle after offset and the tilt angle before offset is as follows:

[0123] γ c =γ' c +γ0 (11)

[0124] To control the lateral deviation with the total lateral offset maneuver Z0 as the target, the lateral stroke Z' needs to be transformed in the reentry coordinate system:

[0125] Z'=Z+Z 0r (12) Z is the lateral range in the reentry coordinate system without considering lateral maneuvering; the lateral maneuvering is defined as positive to the left along the flight path.

[0126] The funnel guidance law under lateral offset maneuvering is given by equations (13) to (15):

[0127]

[0128]

[0129] K5 = C z3 +C z4 (v / v e (15)

[0130] Where v is the velocity relative to the Earth, v e For reentry speed, The derivative of Z', Let K5 be the boundary of the funnel, γ be the tilt angle at the current moment, γ(k-1) be the tilt angle at the previous moment, and C be the tilt angle at the previous moment. z1 C z2 C z3 C z4 This is the lateral guidance coefficient. When the sign of the tilt angle changes, the tilt angle magnitude is:

[0131]

[0132] Where Δt is the control period. γ is the angular velocity of the tilt angle overturning. isThe start roll angle after the sign change is biased. The lateral funnel and lateral deviation after the bias are shown in Figure 6

[0133] S7, accurate solution iteration calculation of braking point position, braking speed increment, roll angle bias amount.

[0134] According to the return reentry trajectory planning basic parameters determined in step S1, the total lateral bias maneuver amount Z0 determined in S3, the braking yaw angle ψ determined in S4, the funnel guidance law in the lateral bias maneuvering determined in S6, the roll angle bias amount initial value in step S5, the braking point relative to the return circle ascending node time t b , the braking on time t p , the braking point longitude λ B and the geocentric latitude , the braking speed increment Δv B , and the roll angle bias amount, the reentry trajectory planning is completed.

[0135] Specifically, the target reentry angle θ e is taken as the iteration target to iteratively solve the braking on time t p , the braking point relative to the return circle ascending node time t b is taken as the iteration target to iteratively solve the roll angle bias amount, the gradient matrix is calculated by using numerical difference, and the gradient iteration algorithm is used to complete the solution. Alternatively, the braking on time t p , the braking point relative to the return circle ascending node time t b , and the roll angle bias amount are taken as optimization variables, the reentry angle θ e is taken as an equality constraint, and the sum of squares of the longitude deviation and the geocentric latitude deviation of the return trajectory terminal and the expected return aiming point is taken as the optimization target, and the sequence quadratic programming algorithm is used to complete the iterative solution.

[0136] Although the present application has been disclosed with the above preferred embodiments, it is not intended to limit the present application, and any person skilled in the art can make possible changes and modifications to the technical solutions of the present application by using the disclosed methods and technical contents without departing from the spirit and scope of the present application. Therefore, any simple modification, equivalent change and modification made to the above embodiments according to the technical essence of the present application, which does not deviate from the technical solutions of the present application, belongs to the protection scope of the technical solutions of the present application.

[0137] The contents not described in detail in the specification of the present application are known to those skilled in the art.​

Claims

1. A method for planning reentry trajectories for strong lateral maneuvers of near-Earth spacecraft, characterized in that, Includes the following steps: S1. Determine the basic parameters for the return reentry trajectory planning, including the orbital inclination angle i0 and the longitude λ of the desired return aiming point. D and geocentric latitude Target reentry angle θ e The initial and terminal values ​​of the reentry phase tilt angle obtained by linear segmentation, the lateral guidance coefficient, and the braking pitch angle. Braking allows for propellant consumption ΔM; S2. Based on the orbital elements of the reentry circle, determine point C on the sub-satellite trajectory, with the same longitude as the desired reentry aiming point, as the reentry aiming point without lateral offset maneuvering. Using the basic parameters for reentry trajectory planning from step S1, calculate the reentry trajectory without lateral offset maneuvering, and output the time t between the braking point and the ascending intersection point of the reentry circle. b Braking start-up time t p Braking point longitude λ B and geocentric latitude Reentry point longitude λ R and geocentric latitude Braking speed increment Δv without lateral offset maneuver B Propellant consumption Δm; S3. Calculate the lateral offset maneuver Z generated by yaw braking based on the linear relationship between propellant consumption Δm, the allowable propellant consumption ΔM for braking, and the propellant consumption corresponding to the lateral deviation during reentry and the lateral braking speed increment. 0b Determine the lateral offset maneuver Z during the reentry phase. 0r The total lateral offset maneuver Z0 is the lateral offset maneuver Z generated by yaw braking. 0b Lateral offset maneuver Z during reentry 0r sum; S4. Based on the return reentry trajectory parameters without lateral offset maneuver output in step S2, calculate the braking yaw angle ψ using spherical trigonometric relations, the relationship between track inclination change and lateral velocity increment. S5. Based on the return reentry trajectory without lateral offset maneuvering from step S2, offset the tilt angle sequence, calculate the corresponding lateral deviation of the aiming point, and determine the lateral offset maneuvering amount Z during the reentry phase based on the linear relationship between the lateral offset of the tilt angle sequence and the lateral deviation of the aiming point. 0r Determine the initial value of the tilt angle offset; S6. Based on the reentry point longitude λ R Reentry point geocentric latitude Establish a reentry coordinate system with the return aiming point C without lateral offset maneuvering. Under the reentry coordinate system, transform the lateral stroke and add a lateral offset maneuver Z during the reentry phase to the funnel boundary of the funnel guidance law without offset. 0r Establish a funnel guidance law under lateral offset maneuvering conditions; S7. Based on the basic parameters for the return reentry trajectory planning determined in step S1, the total lateral offset maneuver Z0 determined in S3, the braking yaw angle ψ determined in S4, and the funnel guidance law under the lateral offset maneuver determined in S6, using the initial value of the tilt angle offset in step S5 and the time t between the braking point and the ascending intersection point of the return loop in S2... b Braking start-up time t p Using the initial values, iteratively solve for the reentry trajectory parameters to complete the reentry trajectory planning.

2. The near-Earth spacecraft strong lateral maneuver reentry trajectory planning method according to claim 1, characterized in that, The calculation of the return reentry trajectory without lateral offset maneuver includes: Braking start-up time t p With the target reentry angle θ e The iterative objective is to solve iteratively using numerical differential gradient or sequential quadratic programming algorithms; the time t between the braking point and the ascending intersection of the return loop is... b The total distance from the braking point to the return aiming point C without lateral offset maneuver is taken as the iterative objective, and is solved iteratively using numerical differential gradient or sequential quadratic programming algorithms. During the iteration process, if t... b >0 Extrapolates the orbit starting from the ascending intersection of the return loop, if t b <0 The trajectory is calculated by reversing the trajectory from the ascending intersection point of the return loop; When the re-entry angle deviation and the total range deviation are both less than the allowable deviation, the iterative calculation stops, the re-entry trajectory parameters are output, and the time t between the final braking point and the ascending node of the return loop is recorded. b Braking start-up time t p Braking point longitude λ B and geocentric latitude Reentry point longitude λ R and geocentric latitude Braking speed increment Δv without lateral offset maneuver B Propellant consumption Δm, latitude argument of braking point u0.

3. The near-Earth spacecraft strong lateral maneuver reentry trajectory planning method according to claim 2, characterized in that, During reentry, the heading guidance employs a gradually decreasing roll angle sequence, while the lateral guidance uses a biasless funnel guidance law.

4. The near-Earth spacecraft strong lateral maneuver reentry trajectory planning method according to claim 3, characterized in that, The lateral offset maneuver Z generated by the yaw braking 0b The calculation method is as follows: Z 0b =(ΔM-Δm)δZ 0b / δΔm δZ 0b δΔm represents the lateral deviation at the reentry terminal and the increased braking propellant consumption.

5. The near-Earth spacecraft strong lateral maneuver reentry trajectory planning method according to claim 4, characterized in that, The reentry phase lateral offset maneuvering Z 0r The solution method is as follows: Let the coefficient 0 < c e <1, the maximum tilt angle offset is c e [90-max(γ' 1s ,γ' 1e )],γ' 1s ,γ' 1e These represent the initial and final values ​​of the first segment of the bank angle straight line, respectively. Based on the calculation results of the maximum bank angle offset and the reentry trajectory without lateral offset, the maximum lateral offset maneuver Z' of the reentry segment is obtained through numerical calculation. 0r According to actual needs, in Z' 0r Determine the lateral offset maneuver Z during reentry within the specified range. 0r .

6. The near-Earth spacecraft strong lateral maneuver reentry trajectory planning method according to claim 5, characterized in that, The method for calculating the braking yaw angle ψ is as follows:

401. Calculate the arc lengths of the three sides of the spherical triangle BCD, where point B is the braking point, point C is the return aiming point without lateral offset maneuvering, and point D is the desired return aiming point. The arc length d of the circular arc BC, expressed in radians, is: The arc length b of the circular arc CD, expressed in radians, is: The arc length c of the circular arc BD, expressed in radians, is: Where, λ B and These are the longitude and geocentric latitude of braking point B, respectively, λ C and λ represents the longitude and geocentric latitude of the return aiming point C without lateral offset maneuvering. D and These are the longitude and geocentric latitude of the desired return aiming point D, respectively; 402. Calculate the track yaw angle Δσ:

403. Calculate the track inclination angle i after yaw braking: i=arccos(cosΔσcosi0-sinΔσsini0cosu0) i0 is the orbital inclination at epoch T0 of the ascending node of the return loop, and u0 is the latitude argument of the braking point; 404. Calculate the normal velocity increment Δv h : μ, p, and r are the Earth's gravitational constant, the semi-orthogonal chord of the orbit before braking, and the distance from the Earth's center to the braking point, respectively.

405. Calculate the braking yaw angle ψ: Δv B For braking speed increments without lateral offset maneuvers, Let y be the braking pitch angle, and arctan2(y,x) be the arctangent function that determines the angle quadrant based on the input y,x.

7. The near-Earth spacecraft strong lateral maneuver reentry trajectory planning method according to claim 6, characterized in that, The initial value of the yaw angle offset is determined as follows: Based on the calculation results of the reentry trajectory without lateral offset, the tilt angle sequence is increased with an offset amount δγ0, and the return reentry trajectory is calculated again to obtain the lateral deviation δZ at the end of the reentry segment. 0r Then the initial value of the tilt angle offset γ0 is: γ0=Z 0r δγ0 / δZ 0r 。 8. The near-Earth spacecraft strong lateral maneuver reentry trajectory planning method according to claim 7, characterized in that, The method for establishing the funnel guidance law under lateral offset maneuvering is as follows: Based on the reentry point longitude λ R Reentry point geocentric latitude Establish a reentry coordinate system with the return aiming point C without lateral offset maneuver, and let the roll angle before offset be γ'. c The tilt angle after offset is γ c Then we have: c c =c' c +γ0 To control the lateral deviation with the total lateral offset maneuver Z0 as the target, the lateral stroke Z' is transformed in the reentry coordinate system: Z'=Z+Z 0r Z represents the lateral stroke in the reentry coordinate system without considering lateral maneuvering; The funnel guidance law under lateral offset maneuvering is as follows: K5=C z3 +C z4 (v / v e ) Where v is the velocity relative to the Earth, v e For reentry velocity, The derivative of Z', Let K5 be the boundary of the funnel, γ be the tilt angle at the current moment, γ(k-1) be the tilt angle at the previous moment, and C be the tilt angle at the previous moment. z1 C z2 C z3 C z4 This is the lateral guidance coefficient; when the sign of the tilt angle changes, the tilt angle size is: Where Δt is the control period. γ is the angular velocity of the tilt angle overturning. is This is the initial tilt angle after the sign is changed following the offset.

9. The near-Earth spacecraft strong lateral maneuver reentry trajectory planning method according to claim 8, characterized in that, When iterating the reentry trajectory parameters in step S7, numerical differential gradient iteration or sequential quadratic programming algorithm is used.

10. The near-Earth spacecraft strong lateral maneuver reentry trajectory planning method according to claim 9, characterized in that, The iterative solution of the reentry trajectory parameters includes: With the target reentry angle θ e The goal of the iteration is to iteratively solve for the braking start-up time t. p The total distance from the braking point to the desired return aiming point is used as the iterative objective to iteratively solve for the time t between the braking point and the ascending node of the return loop. b The total lateral offset maneuver Z0 is used as the iterative target to solve for the tilt angle offset. The gradient matrix is ​​calculated using numerical difference, and the solution is completed using the gradient iteration algorithm. Alternatively, the braking start-up time t p The time t between the braking point and the rising intersection of the return loop b The tilt angle offset is the optimization variable, with the reentry angle θ as the optimization variable. e As an equality constraint, the optimization objective is to minimize the sum of the squares of the longitude deviation and the geocentric latitude deviation between the return trajectory terminal and the desired return aiming point. The sequential quadratic programming algorithm is used to complete the iterative solution.

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