Fastest fuel-optimal on-board autonomous planning method for coplanar flyby of elliptic orbit target

Abstract

The patent discloses a kind of to ellipse orbit same plane target fast companion fly around fly the most fuel-efficient control on-board autonomous planning method, from the same orbit plane fast approach, high-precision companion fly / around fly / sweep fly fuel-saving control on-board autonomous solution method at long distance, comprising: a kind of 3 planning, 5 maneuvering long-distance approach companion fly / around fly / sweep fly configuration formation method is proposed;Propose a kind of two-body model is solved the most fuel-efficient control analytical solution initial value suitable for on-board autonomous solution, high-precision orbit extrapolation model iterative accurate solution final value efficient iteration method.The method is suitable for the fast approach companion fly / around fly / sweep fly of any elliptical orbit satellite to long-distance target on approximate same orbit in near-earth space, and control accuracy can reach ten meters level;And small amount of calculation is suitable for on-board autonomous task planning solution.

Description

TECHNICAL FIELD

[0001] The present application relates to the most fuel-efficient fast formation of the orbiting / around flying / skimming configuration of the elliptical orbit coplanar target. Specifically, it relates to deriving the corresponding relationship between the orbit root number control target and the configuration parameter; proposing an analytical solution method for wide adaptive configuration control according to the coupling characteristics of each orbit root number control; using the analytical solution as the initial value, and using the high-precision orbit extrapolation model to quickly and accurately iterate the initial value, to achieve the most fuel-efficient control under the autonomous solution on the satellite. BACKGROUND

[0002] With the deepening of space applications, more and more spacecrafts use elliptical orbits. For the failure or failure of the elliptical orbit spacecraft (hereinafter referred to as the target), the maintenance spacecraft (hereinafter referred to as the satellite) is in the same orbit as the target but at a long distance. The satellite needs to approach the target at a long distance to form a flying / around flying / skimming observation configuration to measure and diagnose the target. Due to the large fuel consumption of the long-distance fast approach, considering the power system constraints of the satellite, the fuel-saving elliptical orbit coplanar target fast configuration formation planning control problem is studied. Through recent research in related fields, there are many studies on the circular orbit approach problem and the cooperative target formation problem, but there are few studies on the autonomous configuration formation problem of the non-cooperative target of the elliptical orbit failure. SUMMARY

[0003] The purpose of the present application is to provide a fast flying / around flying / skimming most fuel-efficient control autonomous planning method for an elliptical orbit coplanar target, based on the analytical solution of the relative orbit root number transfer problem derived from the Gauss perturbation equation and the kinematic method, an analytical solution method for wide adaptive flying / around flying / skimming configuration formation with 3 times planning and 5 times maneuvering is proposed, and high-precision control is achieved through high-precision orbit extrapolation model iteration.

[0004] In order to illustrate the above-mentioned application, the following technical solutions are adopted in this patent: a fast flying / around flying / skimming most fuel-efficient control autonomous planning method for an elliptical orbit coplanar target, the specific steps are as follows:

[0005] Step 1, based on the relative motion equation of elliptical orbit derived from the kinematic method, the relative orbit root number difference control target of the satellite and the target under the flying / around flying / skimming configuration is derived; the specific method is as follows:

[0006] (1) If the coplanar flying is required, the flying distance is , then the satellite and the target only have the difference in the mean anomaly, and the orbit root number difference control target of the satellite relative to the target is:

[0007]

[0008] (2) If the coplanar around flying is required, the around flying distance is If the satellite and the target only have eccentricity difference, the control target of the orbit root number difference of the satellite relative to the target is:

[0009]

[0010] (3) If coplanar flyby is required, the flyby distance is If the satellite and the target have semi-major axis, eccentricity and argument of periapsis difference, the control target of the orbit root number difference of the satellite relative to the target is:

[0011]

[0012] According to the semi-major axis difference control target and the eccentricity difference control target, the control target of the near and far apogee height difference can be calculated as:

[0013]

[0014] In the formula, represents the average orbit semi-major axis of the spacecraft, represents the eccentricity of the spacecraft, represents the inclination of the spacecraft, represents the ascending node right ascension of the spacecraft, represents the near apogee amplitude angle of the spacecraft, represents the argument of periapsis of the spacecraft, represents the far apogee height of the spacecraft, represents the near apogee height of the spacecraft; subscript represents the target, and superscript represents the control target of the orbit parameter;

[0015] Step two, based on the Gauss perturbation equation, a 3-time planning and 5-time maneuver semi-major axis-eccentricity-latitude amplitude angle joint control analytical solution method is proposed according to the principle of minimum fuel control;

[0016] Step three, according to the sign of the initial orbit root number difference between the satellite and the target, the control time and control direction of the 5-time maneuver can be determined; based on the orbit dynamics equation under the two-body model, considering the engineering constraint conditions, the size of the 5-time maneuver impulse control quantity is solved, and the analytical solution under the two-body model is obtained as the initial value;

[0017] Step four, considering the influence of space perturbation, taking the analytical solution in step three as the initial value, Newton iteration method is used to accurately iterate the finite thrust accurate control sequence by using high-precision orbit extrapolation model.

[0018] Further, the specific method of establishing the 3-time planning-5-time maneuver semi-major axis-eccentricity-latitude amplitude angle joint control strategy in step two is as follows:

[0019] 5-pulse impulsive control strategy is as follows:

[0020] The p1th control is at the apogee, which is fine-tuning control, and the satellite and the target have the same perigee height or apogee height after the control;

[0021] The 1st control is at the perigee, which is approaching control, and the satellite and the target have a semi-major axis difference after the control, and the satellite starts to approach the target;

[0022] The 2nd control is at the perigee, which is deceleration control, and the semi-major axis difference between the satellite and the target is reduced after the control, and the speed of the satellite approaching the target is also reduced;

[0023] The p2th control is at the apogee, which is fine-tuning control, and the satellite and the target have the same perigee height or apogee height after the control; the p2th control and the 3rd control are opposite controls with a control time interval of half an orbit;

[0024] The 3rd control is at the perigee, which is residence control, and the semi-major axis difference between the satellite and the target is zero after the control, and the satellite is in relative residence with the target, and the latitude amplitude angle control is in place;

[0025] When the 5-pulse impulsive control strategy is implemented in orbit, 3 times of planning are adopted:

[0026] In the first planning, the p1th, 1st, 2nd, p2th and 3rd controls are solved, and after obtaining the control sequence, only the p1th and 1st controls are implemented;

[0027] In the second planning, the remaining 2nd, p2th and 3rd controls are solved again, and after obtaining the control sequence, only the 2nd control is implemented;

[0028] In the third planning, the remaining p2th and 3rd controls are solved again, and after obtaining the control sequence, the p2th and 3rd controls are implemented.

[0029] Further, the specific method for solving the analytical solution initial value of the 5-pulse impulsive maneuver based on the two-body model in step three is as follows:

[0030] According to the initial orbit elements of the satellite and the target, the initial orbit element difference of the satellite relative to the target is solved:

[0031] Apogee height difference: ;

[0032] Perigee height difference: ;

[0033] Latitude amplitude angle difference: ;

[0034] In the formula, denotes the difference of the orbit parameters of the satellite relative to the target; denotes the latitude amplitude of the spacecraft, subscript denotes the perigee, denotes the apogee, denotes the target, denotes the satellite, denotes the initial value at a certain moment;

[0035] According to the signs of the height difference between the perigee and the apogee and the latitude amplitude difference , the control time and control direction of the 5-pulse maneuver are determined as shown in the following table:

[0036]

[0037] In the above table: denotes the control time, denotes control at the apogee, denotes control at the perigee; denotes the control direction, denotes control along the transverse direction, denotes control in the opposite transverse direction; denotes the control amount of the th control is 0; denotes the control amount of the p2th control is 0.

[0038] Further, the control amount of the 5-pulse maneuver satisfies the following relationship:

[0039] (1)

[0040] (2)

[0041] (3)

[0042] (4)

[0043] (5)

[0044] In the formula, denotes the orbital angular velocity;

[0045] is the transverse relative motion speed of the satellite relative to the target at the control time of the first control;

[0046] is the transverse distance between the target flying point / circling point / skimming point and the target, and is the arc length, with positive and negative signs;

[0047] is the relative lateral distance of the satellite to the target at the first control time, is the arc length, and has a positive or negative sign;

[0048] is the satellite orbit period after the first, second, and third control, and is related to the lateral control variable ;

[0049] is the number of whole orbits of the satellite after the first, second, and third control, and is selected according to the actual scene;

[0050] is the number of half orbits of the satellite after the first, second, and third control, and is a control variable, ;

[0051] Using the five equations, the control variables of the five-pulse maneuver can be obtained .

[0052] Further, for the method of rapidly iterating the initial value of the control variable using a high-precision orbit extrapolation model, the following is used:

[0053] 1) The control variable initial value solved by the analytical solution, the control directions Dp1, D1, D2, Dp2, and D3, and the control times Pp1, P1, P2, Pp2, and P3, are converted into finite thrust and substituted into the high-precision orbit extrapolation model to extrapolate to the control target formation time , and the orbit root number of the satellite relative to the target at the time is solved; j represents the jth iteration solution;

[0054] 2) Determine whether to stop iteration: if , it indicates that the semi-major axis, eccentricity, and mean anomaly of the satellite are all controlled, i.e., the formation control is completed, and the iteration is stopped;

[0055] 3) Otherwise, update the to-be-controlled variable according to the following formula, and re-solve the initial value and perform the high-precision orbit extrapolation model iteration of step 1);

[0056] .

[0057] The beneficial effect of the present application is to provide a most fuel-efficient control on-board autonomous planning method for fast flying around and flying past the same plane target of the elliptical orbit, aiming at the fast configuration formation demand of the flying around / flying around / flying past the same plane target of the elliptical orbit, considering the spacecraft power system constraint and the most fuel-efficient control principle, proposing a wide adaptive 3-time planning, 5-time maneuvering semi-major axis-eccentricity-latitude amplitude angle joint control analytical solution method; taking the most fuel-efficient semi-major axis-eccentricity-latitude amplitude angle joint control analytical solution as the initial value, using the high-precision orbit extrapolation model to iteratively control the sequence accurately, so as to realize the high-precision closed-loop control under the on-board autonomous planning.

[0058] The method is suitable for fast approaching flying around / flying around / flying past the distant target on the approximate same orbit of the satellite on the near-earth space of any elliptical orbit, and the control accuracy can reach ten meters; and the calculation amount is small, which is suitable for on-board autonomous task planning solution. BRIEF DESCRIPTION OF DRAWINGS

[0059] The drawings of the specification of the present patent mainly assist in understanding the present patent by means of graphs, which specifically include:

[0060] Figure 1 It is a 3-pulse control schematic diagram for the formation of the distant approaching flying configuration;

[0061] Figure 2 It is the change of the relative orbital lateral distance of the satellite and the target with time;

[0062] Figure 3 It is the relative orbital radial distance of the satellite and the target with the lateral distance;

[0063] Figure 4 It is the change of the relative orbital radial distance of the satellite and the target with time. DETAILED DESCRIPTION

[0064] The present application will be further described below in combination with the drawings.

[0065] Firstly, based on the relative motion equation of the elliptical orbit derived by the kinematics method, the relative orbital element difference control target of the satellite and the target under the flying around / flying around / flying past configuration is derived;

[0066] Secondly, based on the Gauss perturbation equation, a 3-time planning, 5-time maneuvering semi-major axis-eccentricity-latitude amplitude angle joint control analytical solution method is proposed according to the most fuel-efficient control principle;

[0067] Then, according to the sign of the initial orbital element difference of the satellite and the target, the control time and control direction of the 5-time maneuvering can be determined; based on the orbital dynamics equation under the two-body model, the size of the 5-time maneuvering pulse control is solved considering the engineering constraint condition, and the pulse control analytical solution under the two-body model is obtained as the initial value;

[0068] Finally, considering the influence of spatial perturbation, the Newton iteration method is used to accurately iterate the finite thrust precise control sequence with the high-precision orbit extrapolation model (HPOP model) as the initial value.

[0069] Further, the specific implementation steps of the technical solution are as follows:

[0070] First, the symbols appearing in the following text are defined:

[0071] Respectively represent: the average orbit semi-major axis of the spacecraft, eccentricity, inclination, ascending node right ascension, perigee amplitude, true anomaly, mean anomaly, latitude amplitude, orbital angular velocity, orbital period, apogee height, perigee height;

[0072] Subscript represents the target, and subscript represents the satellite;

[0073] represents the difference in orbital parameters of the satellite relative to the target;

[0074] Superscript represents the control target of the orbital parameter.

[0075] Step 1: Calculate the satellite relative to the target in the flying / flying / flying configuration Orbit element difference control target

[0076] When the target is an elliptical orbit, the relative motion equation of the satellite (subscript ) in the LVLH coordinate system of the target (subscript ) is derived based on the kinematic method:

[0077] (1)

[0078] Among them: is the average orbit semi-major axis difference, eccentricity difference, inclination difference, ascending node right ascension difference, perigee amplitude difference, and mean anomaly difference of the satellite relative to the target at a certain time;

[0079] (2)

[0080] From this equation, the satellite relative to the target in the coplanar flying / flying / flying configuration Orbit element control target is derived as follows:

[0081] 1) If coplanar flying is required, the flying distance is , then the satellite and the target only have a difference in mean anomaly, and the satellite relative to the target Orbit element difference control target is:

[0082] (3)

[0083] 2) If coplanar flight is required, the flight distance is... If the satellite and the target differ only in eccentricity, then the difference in orbital elements between the satellite and the target controls the target as follows:

[0084] (4)

[0085] 3) If coplanar flyby is required, the flyby distance is... Then, the semi-major axis, eccentricity, and mean anomaly angle of the satellite and the target all differ. The difference in the orbital elements of the satellite relative to the target controls the target as follows:

[0086] (5)

[0087] Based on the above-mentioned semi-major axis difference control target and eccentricity difference control target, the perigee height difference can be calculated. Difference between apogee and altitude Control objectives:

[0088] (6)

[0089] Step 2: Develop a joint control strategy for semi-major axis, eccentricity, and latitude argument with 3 planning phases and 5 maneuvers.

[0090] The 5-pulse maneuver control strategy proposed in this patent is developed based on the 3-pulse maneuver control strategy. Let's first introduce the 3-pulse maneuver control strategy.

[0091] 1.3 Pulse Maneuver Control Strategy

[0092] In the scenario where the satellite and target are initially in the same orbit but differ only in latitude angle, theoretically, the satellite can achieve close-range control of the target using a 2-pulse maneuvering control strategy:

[0093] The first control was an approach control. After the control, there was a half-major axis difference between the satellite and the target, and the satellite began to approach the target.

[0094] The second control is a dwell control, in which the satellite and the target's semi-major axis are equal after control, and the satellite dwells relative to the target, achieving close-range dwelling of the target.

[0095] Considering the measurement and control errors that may occur during the engineering implementation, if the approach distance is relatively long, the control input of the 2-pulse maneuver is large, and there is no opportunity for mid-course correction, making it difficult to achieve high-precision control. Therefore, the dwell control is performed in two stages: first deceleration, then dwell, as follows: Figure 1 The 3-pulse maneuver control strategy shown:

[0096] The first control was an approach control. After the control, there was a half-major axis difference between the satellite and the target, and the satellite began to approach the target.

[0097] The second control is deceleration control, and the semi-major axis difference between the satellite and the target is reduced, and the speed of the satellite approaching the target is also reduced.

[0098] The third control is residence control, and the semi-major axis difference between the satellite and the target is zero, and the satellite is in residence relative to the target, and the latitude amplitude angle control is in place, and the approaching residence of the target is realized.

[0099] Compared with the 2-pulse maneuver control strategy, the 3-pulse maneuver control strategy has higher engineering feasibility. The second control can correct the error accumulation of the first control, and the third control can correct the error accumulation of the second control. The control amount of the third control is usually a small amount relative to the control amount of the second control, and the residual error of the third control is also small, so the control accuracy of the residence point can be guaranteed.

[0100] 2, 5-pulse maneuver control strategy

[0101] If the initial satellite and the target not only have a latitude amplitude angle difference, but also have a certain semi-major axis difference and eccentricity difference, on the basis of the above-mentioned 3-pulse maneuver, a pair of eccentricity control is added to realize the approaching of the target while eliminating the semi-major axis difference and the eccentricity difference, that is, the 5-pulse maneuver control strategy:

[0102] The p1th control is fine-tuning control at the far point, and the near point height or the far point height of the satellite and the target is equal. The p1th control and the first control are opposite controls with a half-orbit interval;

[0103] The first control is approaching control at the near point, and the satellite and the target have a semi-major axis difference, and the satellite begins to approach the target;

[0104] The second control is deceleration control at the near point, and the semi-major axis difference between the satellite and the target is reduced, and the speed of the satellite approaching the target is also reduced;

[0105] The p2th control is fine-tuning control at the far point, and the near point height or the far point height of the satellite and the target is equal. The p2th control and the third control are opposite controls with a half-orbit interval.

[0106] The third control is residence control at the near point, and the semi-major axis difference between the satellite and the target is zero, and the satellite is in residence relative to the target, and the latitude amplitude angle control is in place.

[0107] When the 5-pulse maneuver control strategy is implemented in orbit, three times of planning are usually used:

[0108] The first time of planning is to solve the p1th, first, second, p2th and third controls, and after obtaining the control sequence, only the p1th and first controls are implemented;

[0109] Second time planning, the remaining second, p2, third control re-solve, get control sequence, only the second control implementation;

[0110] Third time planning, the remaining p2 and the third control re-solve, get control sequence, execute p2 and the third control implementation;

[0111] Therefore, called "3 planning, 5 times maneuver".

[0112] It should be noted that the above p1 control and p2 control, in the first planning, only one of them needs control.

[0113] Step 3: based on two body model solution 5 pulse maneuver analytical solution initial value

[0114] Based on two body model and pulse maneuver strategy, solve 5 pulse maneuver analytical solution initial value.

[0115] 1, control timing and control direction determination

[0116] 5 pulse maneuver control timing and control direction can be determined by the satellite and the target of the initial orbit element difference. The initial orbit element difference of the satellite relative to the target is solved by the initial orbit element of the satellite and the target:

[0117] Apogee height difference: ;

[0118] Perigee height difference: ;

[0119] Latitude amplitude angle difference: ;

[0120] In the above formula, subscript P represents perigee, A represents apogee, represents the target, represents the satellite, represents the initial value at a certain time.

[0121] According to the perigee and apogee height difference And the latitude amplitude angle difference The control timing and control direction of 5 pulse maneuver can be determined as shown in Table 1. Among them, P represents the control timing, P=A represents the control at the apogee, P=P represents the control at the perigee; D represents the control direction, D=1 represents the control along the lateral direction, D=-1 represents the control in the opposite direction; represents the control amount of p1 control is 0; represents the control amount of p2 control is 0.

[0122] Table 1

[0123]

[0124] From Table 1, according to the sign values of the initial apogee-perigee height difference and the latitude amplitude difference , there are 8 initial working conditions, and the control strategies can be classified into 4 types:

[0125] (1) Working condition 1:

[0126] The satellite needs to lift the perigee height, and at the same time, the satellite needs to lower the semi-major axis to chase the approaching target. At this time, the control target of the 5-pulse maneuver is:

[0127] The p1th control: should decelerate at the apogee (P = A), and lower the perigee to approach the target. However, lowering the perigee does not have a high efficiency in lowering the apogee, so this control is not controlled, that is, ;

[0128] The 1st control: decelerate at the perigee (P = P), and lower the satellite apogee (D1 = -1) to chase the approaching target;

[0129] The 2nd control: accelerate at the perigee (P = P), and lift the satellite apogee (D2 = 1) to the apogee height of the approaching target;

[0130] The p2th control: accelerate at the apogee (P = A), and lift the satellite perigee (Dp2 = 1) to the perigee height of the target;

[0131] The 3rd control: accelerate at the perigee (P = P), and lift the satellite apogee (D3 = 1) to the apogee height of the target.

[0132] (2) Working condition 2:

[0133] The satellite needs to lift the perigee height, and at the same time, the satellite needs to lift the semi-major axis to lag behind the approaching target. At this time, the control target of the 5-pulse maneuver is:

[0134] The p1th control: accelerate at the apogee (P = A), and lift the satellite perigee (Dp1 = 1) to the perigee height of the target:

[0135] The 1st control: accelerate at the perigee (P = P), and lift the satellite apogee (D1 = 1) to lag behind the approaching target;

[0136] The 2nd control: decelerate at the perigee (P = P), and lower the satellite apogee (D2 = -1) to the apogee height of the approaching target;

[0137] The p2 control: should be in the apogee deceleration (P = A), reduce the satellite perigee to the target height. But given the p1 control has been perigee control in place, so this control is no control, namely ;

[0138] (Note: only the first time planning p2 control is no control; the second time planning, should be solved according to the actual perigee and apogee height difference between satellite and target at the planning time)

[0139] The third control: in the perigee deceleration (P = P), reduce the satellite apogee (D3 = -1) to the target apogee height.

[0140] (3) case 3:

[0141] The satellite needs to reduce the perigee height, and the satellite needs to reduce the semi-major axis to catch up with the target. At this time, the control target of 5 pulse maneuver is:

[0142] The p1 control: in the apogee deceleration (P = A), reduce the satellite perigee (Dp1 = -1) to the target perigee height:

[0143] The first control: in the perigee deceleration (P = P), reduce the satellite apogee (D1 = -1) to catch up with the target;

[0144] The second control: in the perigee acceleration (P = P), lift the satellite apogee (D2 = 1) to the apogee height of the target;

[0145] The p2 control: should be in the apogee acceleration (P = A), lift the satellite perigee to the target height. But given the p1 control has been perigee control in place, so this control is no control, namely ;

[0146] (Note: only the first time planning p2 control is no control; the second time planning, should be solved according to the actual perigee and apogee height difference between satellite and target at the planning time)

[0147] The third control: in the perigee acceleration (P = P), lift the satellite apogee (D3 = 1) to the apogee height of the target.

[0148] (4) case 4:

[0149] The satellite needs to reduce the perigee height, and the satellite needs to lift the semi-major axis to lag behind the target. At this time, the control target of 5 pulse maneuver is:

[0150] The p1th control: should be in the far point acceleration (P = A), lift the near point to approach the target. But given the lifting of the near point is not close to the efficiency of lifting the far point, so this control is no control, namely ;

[0151] The first control: in the near point acceleration (P = P), lift the satellite far point (D1 = 1), to catch up with the target;

[0152] The second control: in the near point deceleration (P = P), reduce the satellite far point (D2 = -1), the far point height of the target;

[0153] The p2th control: in the far point deceleration (P = A), reduce the satellite near point (Dp2 = -1) to the near point height of the target;

[0154] The third control: in the near point deceleration (P = P), reduce the satellite far point (D3 = -1) to the far point height of the target.

[0155] The above four control strategies, the control time of 5 pulse maneuver is always in the near point or the far point, the control direction is always along the transverse or anti-transverse, which meets the principle of minimum fuel consumption of semi-major axis, eccentricity and latitude amplitude angle derived by Gauss perturbation equation.

[0156] 2, pulse maneuver control quantity size solving

[0157] Under the two-body dynamics, after 5 pulse maneuver, the relative orbit element difference of the satellite to the target reaches the orbit element difference control target solved in step 1. Taking this as the constraint condition, the control quantity size of the 5 pulse maneuver of the satellite relative to the target is solved. 、 、 、 、

[0158] (1) terminal semi-major axis constraint

[0159] After 5 pulse maneuver, the semi-major axis of the satellite and the target is equal (companion fly / fly around) or the fly-by height (fly-by), that is, the transverse relative velocity of the satellite relative to the target is zero (companion fly / fly around) or equal to the determined value (fly-by):

[0160] (7)

[0161] In the above formula, j represents the jth iteration solution. is the transverse relative velocity of the satellite relative to the target at the control time of the first control.

[0162] (2) terminal eccentricity constraint

[0163] ​5 After the 5-pulse maneuver, the eccentricity of the satellite relative to the target is equal (co-orbital / flyby) or a determined value (orbiting), i.e. the difference between the apogee and perigee of the satellite relative to the target is zero (co-orbital / flyby) or equal to a determined value (orbiting):

[0164] (8)

[0165] (9)

[0166] (3) Terminal latitude amplitude constraint

[0167] 5 After the 5-pulse maneuver, the satellite reaches the co-orbital point / orbiting point / flyby point:

[0168] (10)

[0169] In the above formula:

[0170] is the transverse distance between the target co-orbital point / orbiting point / flyby point and the target, and is the arc length, with positive and negative signs;

[0171] is the transverse distance of the satellite relative to the target at the first control time, and is the arc length, with positive and negative signs.

[0172] is the orbital period of the satellite after the p1th, 1st, 2nd, p2th, and 3rd control, which is related to the transverse control variable . According to the energy formula, the transverse control variable causing the change in the orbital period can be obtained:

[0173] (11)

[0174] The above formula is derived based on a circular orbit, and has certain errors for an elliptical orbit. The errors can be eliminated through high-precision model iteration. Then can be calculated approximately using the following formula:

[0175] (12)

[0176] wherein and are the orbital intersection period and the semi-major axis of the orbit before the p1th control.

[0177] wherein is the number of whole revolutions of the satellite after the p1th, 1st, 2nd, and p2th control, and the value range thereof is selected according to the actual scenario; is the number of half revolutions of the satellite after the p1th, 1st, 2nd, and p2th control, and the control variable .

[0178] According to the above four working condition analysis, the p1th and p2th control are always at the far point, and the 1st, 2nd and 3rd control are always at the near point; and in order to speed up the near process and reduce the control error accumulation, the p1th control and the 1st control are only separated by half orbit, and the p2th control and the 3rd control are only separated by half orbit, that is:

[0179] (13)

[0180] (4) p1th and p2th control constraints

[0181] According to the above positioning of the p1th control and the p2th control under the four working conditions, for the first planning, the control amount of one of the two controls must be zero, and the rule is: if and have the same sign, the control amount of the p1th control is 0, otherwise the control amount of the p2th control is 0.

[0182] (14)

[0183] According to the above analysis, there are 7 unknowns .

[0184] According to formula (9) and formula (14), the can be uniquely solved.

[0185] According to formula (7), (8) and (10), according to the value range allowed by the actual control scene , set two-layer loop, solve , get a series of feasible solutions.

[0186] After getting the feasible solution value of , according to the principle of the shortest time, the least fuel or the control amount of the last control close to a certain nominal value, determine a set of optimal solutions of the impulsive maneuver under the two-body model :

[0187] (15).

[0188] Step 4: Iterative finite thrust control accurate solution with high-precision orbit extrapolation model

[0189] Taking the least fuel control analytical solution of the orbit plane normal correction and the orbit shape correction in the two-body problem as the initial value, using Newton iteration method, using high-precision orbit extrapolation model (HPOP model) to iterate the accurate solution.

[0190] 1. Solve the control effect of the current control sequence

[0191] Impulsive thrust control sequence initial value solved under two-body model Convert to finite thrust Control duration , the thrust acting duration is evenly distributed before and after the control opportunity. Replace the finite thrust , control duration and control opportunity (or ) into the high-precision orbit extrapolation model (HPOP model) to extrapolate to the control target formation moment , and obtain the target orbit and satellite orbit at this moment.

[0192] Solve the actual orbit element difference of the satellite relative to the target at moment:

[0193] (16)

[0194] Combine the orbit element difference control target determined according to the configuration in the foregoing to solve the orbit element difference of the satellite relative to the target at moment:

[0195] (17)

[0196] 2. Determine whether the control is in place to stop iteration

[0197] Set the judgment threshold of the orbit element difference control in place to determine whether the current control sequence is in place. If is true at the same time, it means that the satellite semi-major axis-eccentricity-latitude amplitude angle joint control is in place, and then the iteration is stopped;

[0198] Otherwise, go to the following steps to continue iteration.

[0199] 3. Re-set the control target to solve the analytical solution

[0200] Update the control target of each orbit element difference of the satellite in step 3 according to the following formula, and re-perform steps 2 and 3 of the two-body model impulsive thrust analytical solution initial value solving and step 4 of the HPOP extrapolation and judgment as described above in 1 and 2.

[0201] (18).

[0202] In order to make the physical law and effect described in the patent easy to understand, the following will further describe the patent combined with specific embodiments.

[0203] Task requirements and input

[0204] This patent is aimed at the formation planning problem of the same plane target of the space elliptical orbit remote approach fly-around fly-by configuration, and the control sequence planning solution suitable for on-board autonomous rapid solution and high precision control is carried out. The task requirements and input conditions are as follows.

[0205] 1. Initial orbit of satellite and target

[0206] The initial orbit of satellite and target is shown in Table 2.

[0207] Table 2

[0208]

[0209] 2. Satellite control system constraints

[0210] The satellite control system constraints are shown in Table 3.

[0211] Table 3

[0212]

[0213] 3. Task target and control threshold

[0214] The task target of the satellite is to achieve 5km fly-around fly-by configuration control of the target. If it is fly-around, the fly-around point is behind the target orbit; if it is fly-by, the fly-by direction is below the target orbit.

[0215] The threshold of each orbit element control of the satellite is set as shown in Table 4.

[0216] Table 4

[0217]

[0218] Task solving results

[0219] 1. Fly-around configuration solving results

[0220] The satellite full process control sequence solution is shown in Table 5.

[0221] Table 5

[0222]

[0223] After the satellite control is completed, the relative orbit lateral distance change of the satellite and the target is as Figure 2 From Figure 2 , the fly-around distance is 5.29km~4.75km, which meets the task requirements.

[0224] 2. Fly-around configuration solving results

[0225] The satellite full process control sequence solution is shown in Table 6.

[0226] Table 6

[0227]

[0228] After satellite control is completed, the radial distance of the relative orbits of the satellite and the target changes with the lateral distance as follows: Figure 3 .from Figure 3 As can be seen from this, the minor semi-axis of the orbital ellipse is 5km, which meets the mission requirements.

[0229] 3. Solution results for the flying configuration

[0230] The solution for the entire satellite control sequence is shown in Table 7 below.

[0231] Table 7

[0232]

[0233] After satellite control is completed, the change in the relative orbital radial distance between the satellite and the target over time is as follows: Figure 4 .from Figure 4 As can be seen, the flyby distance is 5.03km~4.3km, which meets the mission requirements.

[0234] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for the minimum fuel on-board autonomous planning of a fast flyby of an elliptic orbit coplanar target by a chaser spacecraft, characterized in that, The specific steps are as follows: Step one, based on the relative motion equation of elliptical orbit derived by kinematic method, the relative orbit root number difference control target of satellite and target in flying-by / circling-by / skimming-by configuration is derived; the specific method is as follows: (1) if coplanar flying-by is required, the flying-by distance is d, then the satellite and target only have difference in mean anomaly, the orbit root number difference control target of satellite relative to target is: (2) if coplanar circling-by is required, the circling-by distance is d, then the satellite and target only have difference in eccentricity, the orbit root number difference control target of satellite relative to target is: Δa * = 0, Δe * = d / a t , Δi * = 0, ΔΩ * = 0, Δω * = 0, ΔM * = 0 (3) if coplanar skimming-by is required, the skimming-by distance is d, then the satellite and target have difference in semi-major axis, eccentricity and mean anomaly, the orbit root number difference control target of satellite relative to target is: According to the semi-major axis difference control target and eccentricity difference control target as above, the control target of perigee height difference and apogee height difference can be calculated as: where a denotes the mean orbital semi-major axis of the spacecraft, e denotes the eccentricity of the spacecraft, i denotes the inclination of the spacecraft, Ω denotes the longitude of the ascending node of the spacecraft, ω denotes the argument of perigee of the spacecraft, M denotes the mean anomaly of the spacecraft, h A denotes the apogee height of the spacecraft, h P denotes the perigee height of the spacecraft; the subscript t denotes the target, and the superscript * denotes the control target of the orbital parameter; Step two, based on Gauss perturbation equation, a 3-time planning and 5-time maneuver semi-major axis-eccentricity-amplitude angle joint control analytical solution method is proposed according to the principle of minimum fuel control; Step three, according to the sign of the initial orbit root number difference of satellite and target, the control time and control direction of 5-time maneuver can be determined; based on the orbit dynamics equation under two-body model, considering the engineering constraint conditions, the pulse control amount size of 5-time maneuver is solved, the analytical solution under two-body model is obtained as initial value; Step four, considering the influence of space perturbation, the Newton iteration method is used to accurately iterate the finite thrust accurate control sequence by using high-precision orbit extrapolation model as initial value in step three.

2. The method of claim 1, wherein the method is characterized by: The specific method of 3-time planning-5-time maneuver semi-major axis-eccentricity-amplitude angle joint control strategy in step two is as follows: The specific method of 5-pulse maneuver control strategy is as follows: The first p1-time control is at the apogee, which is fine-tuning control, and after the control, the perigee height or apogee height of satellite and target is equal; the first p1-time control and the first-time control are opposite controls with a half-orbit interval; The first-time control is at the perigee, which is approaching control, and after the control, the semi-major axis difference of satellite and target exists, and the satellite begins to approach the target; The second-time control is at the perigee, which is deceleration control, and after the control, the semi-major axis difference of satellite and target is reduced, and the speed of satellite approaching the target is also reduced; The second p2-time control is at the apogee, which is fine-tuning control, and after the control, the perigee height or apogee height of satellite and target is equal; the second p2-time control and the third-time control are opposite controls with a half-orbit interval; The third-time control is at the perigee, which is residence control, and after the control, the semi-major axis difference of satellite and target is zero, and the satellite is relative to the target, and the amplitude angle control is in place; When the 5-pulse maneuver control strategy is implemented in orbit, 3-time planning is adopted: When the first-time planning, the first p1-time, the first-time, the second-time, the second p2-time and the third-time control are solved, and after the control sequence is obtained, only the first p1-time and the first-time control are implemented; When the second-time planning, the remaining second-time, the second p2-time and the third-time control are solved again, and after the control sequence is obtained, only the second-time control is implemented; When the third-time planning, the remaining second p2-time and the third-time control are solved again, and after the control sequence is obtained, the second p2-time and the third-time control are implemented.

3. The method of claim 2, wherein the method is characterized by: The initial value solving method for the analytical solution of 5-pulse maneuver in Step 3 is as follows: The initial orbit root number difference of the satellite relative to the target is solved according to the initial orbit root number of the satellite and the target: Apogee height difference: Ah A = h At - h As ; Perigee height difference: Ah P = h Pt - h Ps ; Latitude amplitude difference: Δu0= u t0 - u s0 ; where Δ(·) = (·) t (·) s denotes the difference in orbital parameters of the satellite relative to the target; u denotes the latitude amplitude angle of the spacecraft, the subscript P denotes the perigee, A denotes the apogee, t denotes the target, s denotes the satellite, and 0 denotes the initial value at a certain time According to the height difference Δh between the near and far points P , Δh A and the sign of the latitude amplitude difference Δu0, the control timing and control direction of the 5-pulse maneuver are determined as shown in the following table: In the above table: P indicates a control timing, P=A indicates control at the apogee, P=P indicates control at the perigee; D indicates a control direction, D=1 indicates control in the lateral direction, D=-1 indicates control in the opposite lateral direction; Δv p1 =0 indicates that the control amount of the p1th control is 0; Δv p2 =0 indicates that the control amount of the p2th control is 0.

4. The method of claim 3, wherein the method is characterized in that: 5 Control amount Δv of pulse maneuver p1 , Δv1, Δv2, Δv p2 , Δv3 satisfy the following relationship: (1) (2) (3) (4) (5) In the formula, n represents the orbit angular velocity; Δv0 is the transverse relative motion speed of the satellite relative to the target at the first control time; L d Ltarget is the lateral distance of the target from the flyby point, in arc length, with a positive or negative sign; L 0t For the first control moment, the lateral distance of the satellite relative to the target is the arc length, which has a positive or negative sign. T p1 , T1, T2, T p2 , T3 is the satellite orbit period after the p1th, 1st, 2nd, p2th, and 3rd control, and is related to the transverse control amount Δv p1 , Δv1, Δv2, Δv p2 , Δv3 Q p1 Q1, Q2, Q p2 p1, p2, p3, p4 are the whole numbers of the first, second, third and fourth control of the satellite operation, and their value ranges are selected according to the actual scene. η p1 , η1, η2, η p2 is the number of semicircles of the satellite's orbit controlled for the p1th, 1st, 2nd, and p2th time, and η = 0 or 1; By using five equations, the control amount Δv of five pulse maneuvers can be obtained p1 , Δv1, Δv2, Δv p2 , Δv3.

5. The method of claim 4, wherein, The method for quickly iterating the control quantity initial value by using a high-precision orbit extrapolation model is as follows: 1) Control variable initial value Δv solved by analytical solution p1 , Δv1, Δv2, Δv p2 , Δv3, control direction Dp1, D1, D2, Dp2, D3, and control timing Pp1, P1, P2, Pp2, P3, are converted into finite thrust, substituted into the high-precision orbit extrapolation model, and extrapolated to the control target formation time t Object , to solve the orbit elements of the satellite relative to the target at time t Object , ΔΔh Pj , ΔΔh Aj , ΔΔM j ; j represents the jth iteration solution; 2) Determine whether to stop iteration: if |ΔΔa j |≤Δa min , |ΔΔe j |≤Δe min , |ΔΔM j |≤ΔM min , it means that the semi-major axis, eccentricity and argument of periapsis of the satellite are all controlled to the desired values, i.e. the formation control is completed, and the iteration is stopped. 3) Otherwise, the to-be-controlled quantity is updated according to the following formula, the initial value solving and the high-precision orbit extrapolation model iteration of Step 1) are re-performed;

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