A distance control method and system for relative motion between satellites

Abstract

The present invention relates to the field of satellite control technology, and discloses a distance control method for relative motion between satellites. The distance between the companion satellite and the reference satellite is reduced by a first position relationship, and the distance between the companion satellite and the reference satellite is increased according to a second position relationship, so that the distance between the satellites can be maintained between a set maximum distance and a set minimum distance. In this way, on the one hand, it is possible to avoid the inter-satellite distance being too large, and ensure that the two satellites are within the maximum distance range required for communication or other cooperative relationships; at the same time, it is possible to avoid the inter-satellite distance being too small, and avoid collisions between the two satellites. The method provided by the present invention can tolerate the influence of satellite orbit perturbations, and allows the inter-satellite distance to vary naturally between the maximum and minimum distances, thereby saving control fuel consumption. The method provided by the present invention only requires relative motion state information between satellites, and does not require precise control of the number of satellite orbit elements, and is simple in motion measurement and control implementation.

Description

Technical Field

[0001] The present invention relates to the field of satellite control technology, and in particular to a distance control method and system for relative motion between satellites. Background Art

[0002] One or more auxiliary satellites are used to accompany the main satellite. Through the collaborative work of the main satellite and the auxiliary satellite, the main satellite's capabilities can be expanded or mission performance can be improved, and even tasks that a single satellite cannot complete can be achieved. This has become a new model for completing space missions. Some close-range multi-satellite collaborative missions require that satellites strictly maintain a prescribed relative motion trajectory, while others only require loose accompanying flight with a bounded distance between satellites. For collaborative missions with strict requirements on relative motion trajectories, since maintaining the prescribed relative motion requires continuous control and consumes more fuel, it is also necessary to release the relative motion trajectory constraints outside the collaborative work period and only maintain a loose accompanying flight state to save fuel.

[0003] Loosely accompanying flight between satellites requires that the relative motion distance is bounded for a long time, that is, the distance between satellites cannot be greater than a certain maximum value to ensure the feasibility of communication or other cooperative relationships between satellites; the distance between satellites cannot be less than a certain minimum value to avoid collision or other interference between satellites. Using a simplified model of the relative motion law of satellites, a bounded relative motion trajectory can be designed, but perturbation or initial relative motion state deviation will cause the relative motion to deviate from the bounded state. Therefore, relative motion maintenance control is also required to maintain the bounded distance accompanying flight for a long time. The existing methods all achieve bounded relative motion between satellites by satisfying matching conditions given under a certain simplified model. These conditions include closed relative motion initial conditions based on the Clohessy-Wiltshire (CW) equation, orbit semi-major axis (energy) matching conditions under the unperturbed model, average orbit element matching conditions, J2 invariant orbit conditions, etc. Among them, the closed relative motion initial conditions and energy matching conditions based on the CW equation will cause a lot of fuel consumption in long-term control because perturbations are not considered. Although the method based on the average orbital element matching condition and the J2 invariant orbital condition takes into account the influence of the J2 term of the earth's non-spherical perturbation and can reduce the fuel consumption for maintaining control, it requires a very high orbital element to maintain control accuracy and places high demands on navigation and control.

[0004] It can be seen that a satellite companion flight distance maintenance control method based on relative motion state, independent of high-precision orbital element information, and capable of fully considering the effects of perturbations to save fuel consumption has yet to be solved. Summary of the invention

[0005] The present invention aims at the distance maintenance control problem of two satellites flying closely together in a near circular orbit, and provides a distance control method and system for relative motion between satellites to solve the problems existing in the prior art.

[0006] In order to achieve the above object, the present invention is implemented by the following technical solutions:

[0007] In a first aspect, the present invention provides a distance control method for relative motion between satellites, comprising:

[0008] Determine a reference satellite and a companion satellite, establish LVLH coordinates with the reference satellite as the center origin, and divide the LVLH coordinates into U quadrant areas in a set plane, where U is a positive integer;

[0009] Determine the instantaneous relative ellipse IRE and the center coordinates (x ct ,y ct ), and according to the center coordinates (x ct ,y ct ) and the positional relationship between the U quadrant areas determine Q first target control areas and W second target control areas, Q and W are both positive integers, and the instantaneous relative ellipse IRE is used to represent the motion trajectory between the companion satellite and the reference satellite;

[0010] reducing the distance between the companion satellite and the reference satellite according to a first positional relationship, wherein the first positional relationship is a positional relationship between the center coordinates of the ellipse IRE and the Q first target control areas;

[0011] The distance between the companion satellite and the reference satellite is increased according to a second positional relationship, wherein the second positional relationship is a positional relationship between the center coordinates of the ellipse IRE and the W second target control areas.

[0012] In a second aspect, an embodiment of the present application provides a distance control system for relative motion between satellites, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the steps of the method described in the first aspect when executing the computer program.

[0013] Beneficial effects:

[0014] The distance control method for relative motion between satellites provided by the present invention reduces the distance between the companion satellite and the reference satellite through the first position relationship, and increases the distance between the companion satellite and the reference satellite according to the second position relationship. In this way, the distance between satellites can be avoided from being too large, ensuring that the two satellites are within the maximum distance range required for communication or other cooperative relationships. At the same time, the distance between satellites can be avoided from being too small, further avoiding the collision between the two satellites. The distance control method for relative motion between satellites provided by the present invention only requires the relative motion state information between satellites, and does not need to accurately control the number of satellite orbital elements, thereby reducing the orbital motion measurement accuracy requirements for control implementation and increasing the simplicity of control implementation; the relative motion control strategy is designed based on the relative motion geometric law under the CW equation, and the maximum and minimum distance constraints between satellites are met by changing the trend of the intersatellite distance change through the relative velocity impulse, allowing the intersatellite distance to change freely within the set range, thereby reducing the control frequency and fuel requirements; the control strategy can tolerate the influence of perturbations, rather than accurately meeting the bounded relative motion conditions under the simplified model, thereby avoiding the additional fuel consumption caused by continuously overcoming perturbation interference. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 A flow chart of a method for controlling the distance of relative motion between satellites according to a preferred embodiment of the present invention;

[0016] Figure 2 This is a schematic diagram of the trajectory and distance variation trend of the IRE central phase diagram of a preferred embodiment of the present invention;

[0017] Figure 3 A schematic diagram of the maximum and minimum distance control strategy on the IRE center phase diagram provided by a preferred embodiment of the present invention;

[0018] Figure 4 A schematic diagram showing the change of normalized distance in the xy plane over time for 300 sample examples provided in a preferred embodiment of the present invention;

[0019] Figure 5 A schematic diagram of the change of the actual distance in the xy plane over time for 300 sample calculation examples provided in the preferred embodiment of the present invention;

[0020] Figure 6 The xy plane relative motion of the first typical sample example provided in the preferred embodiment of the present invention;

[0021] Figure 7 Three control speed impulses of the first typical sample example provided in the preferred embodiment of the present invention; wherein, (a) is the speed impulse in the x direction for IRE size adjustment; (b) is the speed impulse in the y direction for maximum distance control; (c) is the speed impulse in the y direction for minimum distance control;

[0022] Figure 8 The change of relative motion geometric parameters of the first typical sample example provided in the preferred embodiment of the present invention;

[0023] Fig. 9 The IRE center phase diagram motion of the first typical sample example provided by the preferred embodiment of the present invention;

[0024] Fig.10 The relative motion in the xy plane of the second typical sample example provided in the preferred embodiment of the present invention;

[0025] Fig.11 Three control speed impulses of the second typical sample example provided by the preferred embodiment of the present invention; wherein, (a) is the speed impulse in the x direction for IRE size adjustment; (b) is the speed impulse in the y direction for maximum distance control; (c) is the speed impulse in the y direction for minimum distance control;

[0026] Fig.12 The variation of relative motion geometric parameters of the second typical sample example provided in the preferred embodiment of the present invention;

[0027] Fig.13 The IRE center phase diagram motion of the second typical sample example provided for the preferred embodiment of the present invention. DETAILED DESCRIPTION

[0028] The technical solution of the present invention is described clearly and completely below. Obviously, the described embodiments are only a part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0029] See also Figure 1 The present application provides a method for controlling the distance of relative motion between satellites, including:

[0030] Step 101: Determine a reference satellite and a companion satellite, establish a LVLH coordinate system with the reference satellite as the center origin, and divide the LVLH coordinate into U quadrants in a set plane, where U is a positive integer.

[0031] In this step, the reference satellite is one of the two satellites flying together. The reference satellite moves along the natural orbit without any control. The companion satellite in this embodiment is a satellite that moves with the reference satellite. It can be seen that the distance between the two satellites in the embodiment of the present application is adjusted by controlling the companion satellite.

[0032] In addition, the construction method of the LVLH coordinate system is consistent with the existing construction method, and will not be described in detail here. The setting plane may refer to the xy plane, that is, the orbital plane composed of the radial and track directions. In other words, the embodiment of the present application only considers the two-dimensional problem in the xy plane.

[0033] Step 102: Determine the instantaneous relative ellipse IRE and the center coordinates (x ct ,y ct ), and according to the center coordinates (x ct ,y ct ) and the positional relationship between the U quadrant areas determine Q first target control areas and W second target control areas, Q and W are both positive integers, and the instantaneous relative ellipse IRE is used to represent the motion trajectory between the companion satellite and the reference satellite.

[0034] Step 103: Reduce the distance between the companion satellite and the reference satellite according to the first position relationship, where the first position relationship is the position relationship between the center coordinates of the ellipse IRE and the Q first target control areas.

[0035] In this step, the Q first target control areas refer to the maximum distance control areas, that is, in these control areas, the movement trend between the companion satellite and the reference satellite needs to be adjusted to reduce the distance between the companion satellite and the reference satellite.

[0036] Step 104: Increase the distance between the companion satellite and the reference satellite according to the second positional relationship, where the second positional relationship is the positional relationship between the center coordinates of the ellipse IRE and the W second target control areas.

[0037] In this step, the W second target control areas refer to the minimum distance control areas, that is, in the control areas, the movement trend between the companion satellite and the reference satellite needs to be adjusted to increase the distance between the companion satellite and the reference satellite.

[0038] The above-mentioned distance control method for relative motion between satellites is applicable to the distance maintenance control problem of two satellites flying close together in a near circular orbit, wherein close distance can refer to a distance of kilometers or less. The distance between the companion satellite and the reference satellite is reduced by the first position relationship, and the distance between the companion satellite and the reference satellite is increased according to the second position relationship. In this way, the inter-satellite distance can be avoided from being too large, and the two satellites can be ensured to be within the maximum distance range required for communication or other cooperative relationships. At the same time, the inter-satellite distance between the two satellites can be avoided from being too small, further avoiding collisions between the two satellites.

[0039] It should be noted that the linearized approximate model of the relative motion of satellites near a near-circular reference orbit is called the Clohessy-Wiltshire (CW) equation, which can be expressed as:

[0040]

[0041] The model is based on the two-body motion assumption and does not consider the influence of perturbations. It describes the free relative motion of the uncontrolled companion satellite relative to the reference satellite in the local-vertical, local-horizontal (LVLH) coordinate system of the reference satellite. In the formula, x, y, z are the coordinate positions of the reference satellite in the LVLH coordinate system. represents the first-order derivative of the coordinate position in the xy plane with respect to time, represents the second-order derivative of the coordinate position with respect to time, is the average orbital angular velocity of the reference orbit, a c is the semi-major axis of the reference orbit, and μ is the gravitational constant of the Earth.

[0042] The analytical solution of equation (1) can be expressed as:

[0043]

[0044] In the formula, θ t represents the phase of motion in the xy plane, A represents the amplitude of motion in the xy plane, represents the phase of the motion in the z-axis direction, B represents the amplitude of the motion in the z-axis direction, and x ct and ct Respectively represent the two coordinates of the center of relative motion in the xy plane;

[0045] The relative motion geometric parameters satisfy:

[0046]

[0047] Among them, x0, y0, z0 are the positions in the three coordinate directions at the initial time (t=0), are the velocities in the three coordinate directions at the initial moment (t=0), respectively. Formula (2) shows that the relative motion can be decomposed into two independent motions in the orbital plane (xy plane) and perpendicular to the orbital plane (z direction). The free relative motion in the xy plane can be regarded as a moving ellipse, that is, the instantaneous parameters at any time t determine an ellipse, which is called the instantaneous relative ellipse (IRE) in this embodiment. The major axis of the IRE is along the y-coordinate axis and the semi-major axis length is 2A, the minor axis of the ellipse is along the x-coordinate axis and the semi-minor axis length is A, and the center coordinates of the IRE at the initial moment are (xc0 ,y c0 ), the IRE center coordinates at time t are (x ct ,y ct ), the motion phase is θ t , θ0 represents the motion phase in the xy plane at the initial moment. The relative motion in the z direction is a simple harmonic vibration with an amplitude of B and a vibration phase at time t. Represents the motion phase in the z direction at the initial moment.

[0048] It can be seen that for free relative motion, the size of the IRE in the xy plane (expressed by the semi-minor axis length A) remains unchanged, and the x coordinate of the IRE center x ct does not change with time, and y ct It changes linearly at a constant rate, and the rate of change is proportional to the absolute value of the x coordinate of the IRE center at the initial moment |x c0 | is proportional to |. Therefore, the IRE will continue to move along the y-axis at a speed proportional to |x c0 |Directly proportional.

[0049] According to the law of relative motion, the motion in the z direction is periodic, and the inter-satellite distance has no long-term change, while the motion in the xy plane has both periodic motion and long-term drift motion along the y axis. Therefore, this embodiment focuses on analyzing the variation law of the inter-satellite distance in the xy plane. The following describes the variation trend of the relative motion distance in the orbital plane as follows:

[0050] In this embodiment, only the two-dimensional problem in the xy plane is considered. The reference satellite is located at the origin of the coordinate system, and the companion satellite is located at the reference satellite LVLH coordinate system at time t. ct ,y ct ) as the center, with the semi-major axis along the y-axis as 2A and the semi-minor axis along the x-axis as A. The maximum distance from the origin to the IRE at time t is called the maximum IRE distance of the two satellites, denoted by d max (t). The minimum distance from the origin to the IRE at time t is called the minimum IRE distance between the two satellites, denoted by d min (t). Figure 2 The dotted ellipse in the figure is an example of an instantaneous relative motion ellipse, on which the corresponding positions of the maximum IRE distance and the minimum IRE distance are marked. Therefore, the actual distance between the two satellites at time t must be at d min (t) and d max (t). When |x ct| is small, the IRE center changes slowly, the periodic relative motion between satellites is much faster than the drift of the ellipse center position, and the actual maximum distance and actual minimum distance between satellites will be very close to the IRE maximum distance and IRE minimum distance respectively. At this time, the IRE maximum distance and IRE minimum distance can well predict the actual maximum and minimum distances between satellites over a period of time, as well as their changing trends.

[0051] Figure 2 is the IRE center position (x ct ,y ct ) Phase diagram of the change in the xy plane of the reference satellite LVLH coordinate system, where the dotted line with an arrow is the motion trajectory of the IRE center, and the arrow indicates the direction of motion. According to the geometric relationship, when the companion satellite is located near the highest point and the lowest point on the IRE, whichever is farther from the origin, the maximum IRE distance between the two satellites reaches the maximum. If the IRE center is above the x-axis, the highest point of the IRE is farther from the origin, otherwise the lowest point of the IRE is farther from the origin. According to the motion law of the IRE center phase diagram trajectory, it can be seen that the change trend of the IRE maximum distance over time is:

[0052]

[0053] In the formula, Indicates d max The time derivative shows that the change trend of the maximum distance of IRE is determined by the quadrant where the center of IRE is located. Figure 2 The changing trend of the maximum distance of IRE is shown in the four quadrants, where d max ↑ indicates that the maximum IRE distance increases with time, d max ↓ indicates that the maximum IRE distance decreases with time.

[0054] In the phase diagram of IRE center motion, an ellipse is defined with the origin as the center, the x-axis direction as the minor axis direction and the semi-minor axis length as A, and the y-axis direction as the major axis direction and the semi-major axis as 2A. When the IRE center coordinates are located on the ellipse, the IRE passes through the origin, that is, the minimum IRE distance between satellites is zero. Therefore, this ellipse is called the Zero Minimum Distance Ellipse (ZMDE), as shown in Figure 2 When the IRE center coordinates are outside the ZMDE, the reference satellite (the origin of the coordinates) is outside the IRE, and the IRE center is in the first and third quadrants. min (t) decreases with time, when the IRE center is in the second and fourth quadrants min (t) increases with time. When the IRE center is located inside the ZMDE, the trend of the IRE minimum distance change is exactly opposite to that when the IRE center is located outside the ZMDE in the same quadrant.

[0055] The curve equation of the ZMDE in the first quadrant is y ct =y ZUL (x ct ), and y ZUL (x ct ) is denoted as x ZUL (y ct ),in:

[0056]

[0057] Therefore, the variation law of the minimum distance of IRE on the phase diagram can be expressed as follows, where Indicates d min Derivative with respect to time:

[0058]

[0059] Figure 2 The middle mark shows the changing trend of the minimum distance of IRE when the IRE center is located in different areas, where d min ↑ indicates that the minimum IRE distance increases with time, d min ↓ indicates that the IRE minimum distance decreases with time.

[0060] In this embodiment, the goal is to maintain long-term companion flight between satellites with low fuel consumption rather than strictly maintaining a specific relative geometric configuration. The constraints for companion flight maintenance are maintaining the feasibility of communication or other cooperative relationships between satellites and avoiding collisions. Among them, communication or other cooperative relationships between satellites limit the maximum distance between satellites, while collision avoidance constraints limit the minimum distance between satellites.

[0061] During the long-term relative motion between satellites, perturbation or initial relative motion state deviation may cause the inter-satellite distance to increase or decrease. When the inter-satellite distance is too large or too small, in order to maintain the inter-satellite cooperative relationship or avoid collision, it is necessary to change the inter-satellite distance change trend through control. Due to the independence and drift-free nature of the z-direction motion, no control is required for stable accompanying flight. Therefore, this embodiment only considers the distance control strategy in the xy plane. According to the above analysis, the inter-satellite distance change trend in the xy plane is determined by the IRE center coordinate position. Therefore, by changing the position of the IRE center, the inter-satellite distance can have a desired change trend.

[0062] According to the expression of the IRE center coordinate position in formula (3), at time t, by changing the relative motion speed in the y direction You can change the IRE center x coordinate x ct , but will not change y ct Similarly, by changing the relative speed in the x direction You can change the IRE center y coordinate y ct , but will not change x ct In this embodiment, the subscript t represents the value of a variable at time t.

[0063] If the expected values ​​of the adjusted x and y coordinates of the IRE center at time t are and The two coordinate changes are and The corresponding y-direction velocity increment and x-direction velocity increment required at time t are

[0064]

[0065] It can be seen that the required velocity impulse is proportional to the change in the IRE center coordinates and has nothing to do with the current IRE center coordinate position.

[0066] In addition, the change of speed will cause the change of IRE size A. From formula (3), we can get

[0067]

[0068] In the formula, x t represents the x-coordinate of the satellite position at time t, y t represents the y coordinate of the satellite position at time t;

[0069] So when the IRE center position changes by Δx ct and Δy ct When the required velocity increment is applied, the IRE semi-minor axis becomes:

[0070]

[0071] Optionally, the U quadrant areas include a first quadrant area, a second quadrant area, a third quadrant area, and a fourth quadrant area, and reducing the distance between the companion satellite and the reference satellite according to the first position relationship includes:

[0072] At the instantaneous relative ellipse IRE, the center coordinate is located at x ct ≤0 and y ct ≥y max (x ct ) or in the region of x ct >0 and y ct ≤-y max (-x ct ), adjust the x in the center coordinates ct -sign(x ct )ε x , where sign() represents the sign function.max (x ct ) is the maximum distance boundary function, which is the solution y of the following equation ct (x ct ):

[0073]

[0074] Two maximum distance boundary curves y ct =y max (x ct ) and y ct =-y max (-x ct )exist Figure 3 Indicated by dotted lines.

[0075] In this optional implementation, two methods of changing the IRE center coordinate position can be used to control the maximum inter-satellite distance. One control method is to change y ct The value of y ct Adjust to the appropriate coordinate position in the opposite direction of the phase trajectory to directly reduce the maximum IRE distance. In order to reduce the frequency of adjustment control, this method needs to adjust the y when the maximum IRE distance is reached. ct Adjust to the coordinate position with the same value and opposite sign, that is, the maximum IRE distance at the other end of the trajectory. After that, as the IRE center moves along the natural trajectory, the maximum IRE distance first decreases. When the IRE center crosses the x-axis, the maximum IRE distance begins to increase until it increases to D max You need to apply y again ct Adjust the impulse control. When |x ct When | is small, the required y ct The adjustment amount is approximately 2(D max -2A).

[0076] The second method of controlling the maximum distance between satellites is to max and When the control action is applied This can be done by changing x ct The symbol is implemented. Figure 3 As shown, when the IRE center is in the 2nd or 4th quadrant, and d max Increase to the limit threshold D max When x is changed by impulse control ct The sign of makes the IRE center enter the 1st or 3rd quadrant respectively. Due to the change in the direction of motion of the phase diagram trajectory, the maximum IRE distance will gradually decrease. When the subsequent free motion of the IRE center crosses the x-axis, the maximum IRE distance will gradually increase until it reaches D at the other end of the phase diagram trajectory. max , you need to change x again ctImpulse control of symbols.

[0077] In order to reduce the impulse control frequency of changing the IRE center coordinate position, it is hoped that y ct The drift rate is relatively slow, that is, it is required that |x ct | is small. Therefore, for both control methods, it is necessary to first ct The value of | is adjusted to a small amount ε x , ε x > 0. After that, the first adjustment y ct In the control method, the adjustment required for each round-trip motion cycle of the phase trajectory is approximately Δy ct =2(D max -2A), the second adjustment x ct In the control method, the adjustment amount per cycle is Δx ct =4ε x According to the IRE center coordinate adjustment amount required by the two methods, it can be seen from formula (7) that the velocity impulse consumed by the first method is much greater than that of the second method. Therefore, as a preferred implementation, the impulse can be used to adjust the IRE center x coordinate. By changing x ct A method for controlling the maximum inter-satellite distance is proposed in which the sign of IRE is changed to change the trend of the maximum distance change.

[0078] It should be noted that the maximum distance control strategy of this embodiment assumes that D max >2A, because when 2A>D max When the relative motion amplitude is too large, the maximum distance between the satellites cannot be less than D max .

[0079] In theory, when x ct = 0, the center position of IRE remains unchanged, d max and d min However, this is only an ideal situation that can be achieved under the CW equation model. In fact, the model has linearization errors and does not consider the influence of various perturbations. In the control implementation, there are also various uncertainties and errors. Therefore, it is necessary to accurately maintain x ct = 0 does not guarantee d max More importantly, under the periodic perturbation of the non-spherical J2 term of the Earth, x is always accurately maintained. ct = 0, which will lead to a lot of unnecessary fuel consumption. The goal of adjusting the control in this embodiment is not to set |x ct | remains at zero, but is adjusted to a small value ε x ε x The size of should be large enough to overcome the perturbation interference, so that the maximum IRE distance still has The trend of change, at the same time ε x should be as small as possible to make yct The drift rate is small, so that the time interval from the IRE center moving along its natural trajectory to the time when the next maximum distance control is required is as long as possible, thereby reducing the frequency of impulse control and the total fuel consumption.

[0080] In summary, the maximum distance control strategy given is: when the IRE center is located at x ct ≤0 and y ct ≥y max (x ct ) or in the region of x ct >0 and y ct ≤-y max (-x ct ), the IRE center x coordinate is adjusted by:

[0081] Δx ct =-sign(x ct )(|x ct |+ε x ) (11)

[0082] The implementation of this adjustment requires applying a velocity impulse along the y direction, and the required velocity impulse is calculated using formula (7).

[0083] Optionally, increasing the distance between the companion satellite and the reference satellite according to the second position relationship includes:

[0084] When the center coordinate of the instantaneous relative ellipse IRE is located in the first control area, the x in the center coordinate is adjusted. ct is a first preset value;

[0085] When the center coordinate of the instantaneous relative ellipse IRE is located in the second control area, the x in the center coordinate is adjusted. ct is a second preset value;

[0086] The first partial control area is a partial control area among the W second target control areas, and the second partial control area is the remaining control areas among the W second target control areas except the first partial control area.

[0087] Among them, the first preset value is ε x , the second preset value is -ε x , the default value ε x It can be selected through simulation tests. For example, a distance between 2 meters and 3 meters can meet the requirements.

[0088] Optionally, the W second target control areas include six control areas, namely a first control area, a second control area, a third control area, a fourth control area, a fifth control area and a sixth control area;

[0089] The starting curve of the first control area is y ct =2A+D min , the termination curve is y ct =2A;

[0090] The starting curve of the second control area is The termination curve is

[0091] The starting curve of the third control area is The termination curve is

[0092] The starting curve of the fourth control area is y ct =-2A-D min , the termination curve is y ct = -2A;

[0093] The starting curve of the fifth control area is The termination curve is

[0094] The starting curve of the sixth control area is The termination curve is

[0095] Where A is the length of the semi-minor axis of IRE, D min Indicates the minimum safe distance between the two stars. represents the function that defines the minimum distance control starting curve outside the ZMDE, represents the function that defines the minimum distance control termination curve outside the ZMDE, represents the function that defines the minimum distance control starting curve in ZMDE, Represents the curve function that defines the minimum distance control termination within the ZMDE.

[0096] Optionally, increasing the distance between the companion satellite and the reference satellite according to the second positional relationship between the center coordinates of the ellipse IRE and the W control areas includes:

[0097] When the center coordinate of the ellipse IRE is located in any one of the first control area, the third control area or the fifth control area, the x in the center coordinate is adjusted. ct is a first preset value;

[0098] When the center coordinates of the ellipse IRE are located in any one of the second control area, the fourth control area or the sixth control area, the x in the center coordinates is adjusted. ct is the second preset value.

[0099] In this optional implementation, it should be noted that in order to avoid collision, the minimum IRE distance d min , so that it is not less than the given threshold value D min Since the minimum distance between satellites depends on the distance between the IRE center and ZMDE, the minimum distance between satellites can be controlled by adjusting the coordinate position of the IRE center to avoid it being too close to ZMDE.

[0100] When the minimum inter-satellite IRE distance d min Reduced to D min When approaching, choose to change the IRE center x coordinate x ct The impulse control method of the sign makes The value of changes from negative to positive to limit the minimum distance between satellites. At the same time, the IRE center target position adopts a smaller x coordinate value, that is, To reduce the drift rate of the adjusted IRE center y coordinate, thereby reducing the frequency of impulse control. Therefore, the minimum distance control strategy depends on the location of the IRE center. According to the phase diagram motion law of the IRE center coordinate, when x ct ≥A+D min or x ct ≤-AD min When IRE minimum distance d min No less than D min , so no control is required; when the IRE center is within the ZMDE of the first and third quadrants, The intersatellite distance will gradually increase, so there is no need to impose minimum distance control; when the IRE center is outside the ZMDE of the first or third quadrant, and inside the ZMDE of the second or fourth quadrant, there is Need to be in d min Reduced to near D min Apply control to avoid collision.

[0101] The closest distance between the first quadrant ZMDE and ZMDE is D min The boundary curve is defined as in is the solution y of the following equation ct (x ct ):

[0102]

[0103] When A>D min When the closest distance to ZMDE in the first quadrant ZMDE is D min The boundary curve is defined as in is the solution y of the following equationct (x ct ):

[0104]

[0105] The two boundary curves are Figure 3 Indicated by dotted lines.

[0106] The designed IRE minimum distance control strategy includes the following six IRE center control areas: ct Adjustment.

[0107] First control area: And 2A<y ct ≤2A+D min ,in Satisfies the following relationship:

[0108]

[0109] According to the law of the natural trajectory of the IRE center moving along the y-axis, the boundary where the IRE center enters the area is defined as the control starting curve of the area, that is, y ct =2A+D min , define the boundary where the IRE center leaves the region as the control termination curve of the region, that is, y ct =2A. When the IRE center is within the control area, the minimum distance control strategy is: ct Adjust to -ε x Place.

[0110] Second Control Area: and in:

[0111]

[0112] as well as

[0113]

[0114] Only when A>D min The control area is only valid when The control termination curve is When the IRE center is within the control area, the minimum distance control strategy is: ct Adjust to ε x Place.

[0115] The third control area: 0≤x ct ≤A and in:

[0116]

[0117] as well as

[0118]

[0119] Only when A>D min The control area is only valid when The control termination curve is When the IRE center is within the control area, the minimum distance control strategy is: ct Adjust to -ε x Place.

[0120] Fourth Control Area: And -2A>y ct ≥-2A-D min The control starting curve of this area is y ct =-2A-D min , control the termination curve to be y ct =-2A. When the IRE center is within the control area, the minimum distance control strategy is: ct Adjust to ε x Place.

[0121] Fifth Control Area: and

[0122] Only when A>D min The control area is only valid when The control termination curve is When the IRE center is within the control area, the minimum distance control strategy is: ct Adjust to -ε x Place.

[0123] Sixth control area: 0>x ct ≥-A and Only when A>D min The control area is only valid when The control termination curve is When the IRE center is within the control area, the minimum distance control strategy is: ct Adjust to ε x Place.

[0124] The six control areas and their boundary curves are as follows: Figure 3 The corresponding minimum distance control strategy adjustment target and direction are shown in Figure 3The horizontal dashed arrow with a dot at the beginning indicates the target position of the IRE center adjustment. The dot at the beginning of the arrow indicates the position of the IRE center before adjustment. The dotted dashed line in the figure indicates various control start curves, and the square dotted dashed line in the figure indicates various control end curves. The vertical dashed arrow in the figure indicates the natural motion trajectory of the IRE center. It should be noted that in order to show a more comprehensive display, Figure 3 The minimum distance control strategy diagram given in the figure is for A>D min When A≤D min When the third control area and the sixth control area do not exist, the control strategies corresponding to the second control area and the fifth control area are invalid.

[0125] The minimum distance control strategy in each control area mentioned above uses the IRE center x coordinate adjustment on the control start curve to immediately change the IRE center position when the phase diagram trajectory reaches the curve, ensuring that the adjusted d min ≥D min , and make From negative to positive, the IRE center x coordinate adjustment in the area between the control start curve and the control end curve cannot ensure that the inter-satellite distance is less than D min , but can make This allows the relative movement to automatically escape from the collision danger zone.

[0126] It is worth noting that there are four smaller risk areas on the IRE central phase diagram:

[0127]

[0128] (2)0≤x ct ≤ε x And -y ZUL (x ct )≤y ct <-y ZUL (ε x );

[0129]

[0130] (4)0≥x ct ≥-ε x And y ZUL (-x ct )≥y ct >y ZUL (ε x );

[0131] in:

[0132]

[0133] When the IRE center is located in these four small areas, as the natural trajectory of the phase diagram moves, the distance between the IRE center and ZMDE will be less than D min , that is, there is a possibility of collision between satellites. The IRE minimum distance control is not applied in these four small risk areas because when the IRE center is located in these risk areas, the x ct Adjust to ±ε x On the other hand, according to the motion law of the phase diagram trajectory and the control strategy design, the IRE center will not return to these four small risk areas after leaving them along the natural trajectory. Therefore, other emergency reactive collision avoidance control methods can be used in practical applications to make the IRE center leave these four small risk areas without collision, thus simplifying the minimum distance control strategy.

[0134] According to the definition of the trajectory movement trend of the IRE center phase diagram and the minimum distance control strategy, as long as the IRE center is located in the safe area on the phase diagram at the beginning, the minimum distance control strategy can ensure that the IRE center is always in the safe area at all times, that is, it can maintain d min ≥D min Among them, the safe area of ​​the IRE central phase diagram is the distance from ZMDE greater than D min And in areas outside the four risk areas mentioned above where there is no minimum distance control.

[0135] If A≤D min , and the IRE center is located at a distance from ZMDE less than D min When the minimum distance control strategy of the second control area, the third control area, the fifth control area and the sixth control area is invalid, and d cannot be achieved in time. min >D min At this time, adjust the IRE size to make A>D min , and then the above minimum distance control strategy can be applied.

[0136] Optionally, before reducing the distance between the companion satellite and the reference satellite according to the first position relationship, the method further includes:

[0137] Determine a first target time period for reducing the distance between the companion satellite and the reference satellite and a second target time period for increasing the distance between the companion satellite and the reference satellite; in the first target time period and the second target time period, a change in the size of the instantaneous relative ellipse IRE caused by adjusting the central coordinates of the instantaneous relative ellipse IRE is within a preset range;

[0138] The reducing the distance between the companion satellite and the reference satellite according to the first position relationship comprises:

[0139] reducing the distance between the companion satellite and the reference satellite during the first target time period;

[0140] The increasing the distance between the companion satellite and the reference satellite according to the second position relationship comprises:

[0141] The distance between the companion satellite and the reference satellite is increased during the second target time period.

[0142] It should be noted that reducing or increasing the inter-satellite distance is achieved by changing the trend of distance change between satellites. The reduction or increase referred to in the embodiment of the present application cannot directly cause a sudden increase or decrease in the distance. The increase or decrease in the distance will continue for a period of time with natural movement. Therefore, in the embodiment of the present application, the increase or decrease of the inter-satellite distance is achieved by adjusting the trend of distance change. In the embodiment of the present application, the timing of maximum distance control and minimum distance control, that is, the execution time period, is determined according to the condition that the adjusted IRE size cannot increase or decrease, and its purpose is to ensure that the change of the adjusted IRE size will not affect the realization of the control target. Among them, the timing of maximum distance control, that is, the requirement of the first target time period is that the adjusted IRE size cannot increase. There are two situations for the timing of minimum distance control, that is, the second target time period: when the target position of the IRE center adjustment control is within the ZMDE, the IRE size is required not to decrease; when the target position of the IRE center adjustment control is outside the ZMDE, the IRE size is required not to increase. If the IRE size cannot be reduced after adjustment, the condition of formula (24) must be met to execute control; if the IRE size cannot be increased, the conditions of formula (26) and formula (27) must be met at the same time to execute control.

[0143] In addition, it is worth noting that the size of IRE, that is, the length A of the semi-minor axis, can be changed by changing the center coordinate of IRE. According to equations (8) and (9), to achieve the same change in A, the change Δx required to adjust the x coordinate of the center of IRE is ct The change Δy required to adjust the y coordinate of the IRE center ct According to formula (7), the same Δx ct and Δy ct The required velocity impulse is the same, so the IRE center x coordinate change Δx is implemented ct It is more fuel-efficient to adjust the IRE ellipse size. However, in |x ct | is small, Δx is applied to change A ct Will increase |x ct |, causing Δy ct The drift speed increases, which will lead to additional control fuel consumption. ctTo adjust the IRE size, take Δx ct =0.

[0144] Assume that the IRE size before adjustment is A, and the IRE size after adjustment is A + =A d , when Δx ct = 0, according to equations (8) and (9), the equation is as follows:

[0145]

[0146] In the formula, represents the y coordinate of the companion satellite relative to the center of IRE, A d represents the length of the expected adjusted IRE semi-minor axis;

[0147] in Take |Δy from the two roots of equation (20) ct |The smaller one, the IRE center y coordinate adjustment amount can be obtained as

[0148]

[0149] When A>A d To ensure the existence of the solution given by equation (21), the following conditions must also be met:

[0150]

[0151] because The maximum value of is 2A, so there is always a Δy that satisfies the condition of formula (22) ct Implement timing to reduce IRE size.

[0152] According to formula (21), Therefore That is x t -x ct = 0, IRE size adjustment is performed, and the required adjustment amount |Δy ct | minimum, the IRE center y coordinate adjustment amount at this time is:

[0153]

[0154] This most fuel-efficient adjustment strategy can be used in non-emergency situations.

[0155] When 2A>D max When A<D, no matter where the IRE center is located in the phase diagram, the control of reducing the IRE size must be implemented, that is, its control area is the entire phase diagram plane. min When the IRE center is inside ZMDE, or outside ZMDE and the minimum distance to ZMDE is less than D minIf the IRE size is within the range of , it is necessary to implement the control of increasing the IRE size; otherwise, there is no need to increase the IRE size. Therefore, the control area where the IRE size needs to be increased on the phase diagram is defined as follows:

[0156] 0≤x ct ≤A+D min and

[0157] and -AD min ≤x ct <0 and

[0158] In applying x ct After the impulse adjustment, the size of IRE may change, so the adjusted IRE center x coordinate may deviate from the expected position relative to the new IRE, resulting in the maximum inter-satellite IRE distance and the minimum IRE distance not meeting the requirements. According to formula (9), given the IRE center position (x ct ,y ct ) and the IRE center x coordinate adjustment Δx ct , the size of the ellipse after adjustment and the coordinate position of the satellite at the time of adjustment (x t ,y t This embodiment provides a restriction condition on the coordinate position of the satellite at the time of applying the impulse, so that the change of the IRE size after adjustment does not affect the control target.

[0159] There are two requirements for limiting the size of the adjusted IRE. One is that the IRE cannot increase, and the other is that the IRE cannot decrease. Comparing equations (8) and (9), we can see that in Δy ct = 0, if a given Δx is required ct The semi-minor axis A of the posterior IRE cannot be reduced, it only needs to satisfy:

[0160] (x t -x ct )·Δx ct <0 (24)

[0161] According to the periodic motion characteristics of the satellite on the IRE, the timing condition of equation (24) can be satisfied for half of the orbital period. On the other hand, if a given Δx is required ct If the semi-minor axis A of the posterior IRE cannot be increased, the following conditions must be met:

[0162] |x t -x ct |≥|x t -x ct -Δx ct | (25)

[0163] That is, satisfying

[0164] (x t -x ct )·Δx ct >0 (26)

[0165] and

[0166] |Δx ct |≤2|x t -x ct | (27)

[0167] According to the periodic motion characteristics of the satellite on IRE, the timing condition of equation (26) can be satisfied for half of the orbital period. t -x ct The maximum value of | is A, so when |Δx ct |When the following relationship is satisfied:

[0168] |Δx ct |<2A (28)

[0169] In the half orbital period that satisfies the condition of equation (26), there is always a period of time during which |x t -x ct | is close to its maximum value A, and the condition of formula (27) can also be satisfied, so that the size of IRE does not increase after adjustment.

[0170] For the above minimum distance control strategy, the minimum IRE distance between satellites after adjustment is affected by the change of ZMDE size (same as IRE size). When implementing the adjustment impulse, it is necessary to avoid that the adjusted IRE minimum distance is less than the expected value of the adjustment target due to the change of IRE size. When the target position of the IRE center adjustment is within the ZMDE, that is, for the second control area, the third control area, the fifth control area and the sixth control area, the adjusted IRE size is required not to be reduced. To this end, it is only necessary to apply the IRE center adjustment impulse when the condition of formula (24) is met, and such a control opportunity must exist within an orbital cycle. When the target position of the IRE center adjustment is outside the ZMDE, that is, for the first control area and the fourth control area, the adjusted IRE size is required not to increase. The minimum distance control strategy for the first control area and the fourth control area, the IRE center x coordinate adjustment amount satisfies the restriction condition of formula (28), so as long as the control impulse is applied at the time when the conditions of formula (26) and formula (27) are met, it can be ensured that the IRE size will not increase.

[0171] For the maximum distance control strategy given above, it is required to implement x ct After adjustment, the IRE dimension A cannot be increased, otherwise the increase in A after adjustment will cause the d max Increase may lead tomax >D max . Considering the satellite's accompanying motion|x ct | is small, so the adjustment amount |Δx ct | is also small, so the condition of equation (28) can be satisfied. If |x ct | If the coordinate is too large, the relative motion drifts too fast, and it must first be adjusted to a smaller value so that the relative motion enters a slow drifting accompanying flight state. Therefore, as long as the maximum distance control impulse is applied when the conditions of equations (26) and (27) are met, the IRE size can be guaranteed not to increase.

[0172] According to the above analysis, the control impulse cannot be implemented immediately when the IRE center reaches the maximum distance control and minimum distance control boundaries. It must also wait for the implementation time specified by the IRE size limit, and the waiting time will not exceed 1 orbital cycle at most. During this waiting time, the y coordinate of the IRE center will drift, so it may cause the IRE center to leave the control area defined by the minimum distance control strategy when the control is implemented, thereby applying invalid control, or the distance constraint has been violated when the control is implemented. In order to avoid control failure caused by the delay in the implementation of the IRE center adjustment impulse, it is necessary to consider the lead time in the design of the distance control strategy. The method is to move the starting boundary of various control areas, that is, the above-mentioned minimum distance control starting curve, forward in the opposite direction of the IRE center trajectory movement by the drift distance of the IRE center y coordinate in 1 orbital cycle. According to formula (3), the drift distance can be obtained as 3πx ct Therefore, the starting curves of various IRE center control areas considering the advance amount can be uniformly expressed as:

[0173] y ct =y B (x ct )+3πx ct (29)

[0174] where y B (x ct ) is the maximum distance control boundary function, and the control starting curve function of the six minimum distance control areas, and π represents the pi constant. In the above-mentioned control method for changing the IRE size, the control area for reducing the IRE size control is the entire phase plane, and the control for increasing the IRE size has no implementation time limit, so there is no need to consider the lead time for the control of changing the IRE size.

[0175] Furthermore, the feasibility conditions of distance keeping control are as follows:

[0176] According to the maximum control strategy design, when D max >2A, by ct1 impulse adjustment can make the IRE center enter x ct = ±ε x and:

[0177] -y max (-ε x )≤y ct ≤y max (-ε x ) (30)

[0178] The maximum distance is determined by the steady-state trajectory range with an upper limit, and the IRE center is controlled by quasi-periodic impulse to circulate on the trajectory to achieve maximum distance maintenance; and when D max <2A, it is necessary to reduce the IRE size to 2A<D max , only then can the maximum distance be maintained.

[0179] According to the minimum distance control strategy design, when A>D min When x ct One impulse adjustment (which may require the assistance of other emergency response collision avoidance controls) can make the IRE center enter x ct = ±ε x and:

[0180] y ct ≤-2A-D min ∨y ct ≥2A+D min (31)

[0181] In the formula, ∨ represents the logical OR operation. Or enter x ct = ±ε x and:

[0182]

[0183] The minimum distance is determined on the steady-state trajectory with a lower bound; and when A<D min To ensure that the distance between stars is not less than the lower bound D min , the IRE center can only enter the steady-state trajectory range defined by equation (31).

[0184] Only when the steady-state trajectories of the maximum distance control and the minimum distance control intersect, the given distance keeping control strategy can keep the inter-satellite distance at D min and D maxAt this time, according to the phase diagram trajectory motion and control strategy design, no matter where the IRE centers of the two satellites are located at the beginning, under the given control strategy, the IRE center trajectory motion will inevitably reach one of the three steady-state control loops corresponding to the intersection of the maximum distance control and minimum distance control steady-state trajectories, and circulate along it. Among the three steady-state control loops, one is located inside the ZMDE, and the other two are located on the upper and lower sides outside the ZMDE. Figure 3 In the figure, the bold vertical virtual arrow line segment (located at x ct = ±ε x The natural trajectory of the vehicle) and the bold horizontal dashed arrow line with a dot at the beginning (control adjustment line) show the composition and position of the three steady-state control loops.

[0185] The conditions that can ensure the existence of two steady-state control loops outside ZMDE are:

[0186] D max >2A∧2A+D min <y max (-ε x ) (33)

[0187] In the formula, ∧ represents the logical AND operation.

[0188] Considering ε x For a small amount, there is y max (-ε x )≈D max -2A, so the condition of formula (33) can be approximately expressed as:

[0189] D max -2A>2A+D min (34)

[0190] The conditions that can ensure the existence of a steady-state control loop within ZMDE are:

[0191] D max >2A∧A>D min (35)

[0192] It can be seen that as long as one of the conditions in (33) and (35) is satisfied, distance keeping control is feasible. The above conditions also show that only D max >5D min When , there is a suitable A that satisfies both equations (34) and (35), that is, the internal and external steady-state control loops can exist at the same time; when 5D min ≥D max >2D min When , for the same A, at most one of equations (34) and (35) is satisfied, that is, only one of the inner and outer steady-state control loops can exist at the same time; when 2D min ≥Dmax >D min When D max >D min In theory, the inter-satellite distance can be kept at D by adjusting the IRE size and controlling the maximum and minimum distances. min and D max in the range between.

[0193] In a complete embodiment, consider two satellites flying together near a circular reference orbit at an altitude of 500 km. The leader satellite moves freely on the reference orbit, and the initial orbital elements of the reference orbit are given: the semi-major axis is 6878137m, the eccentricity is 0, the orbital inclination is pi / 6, the right ascension of the ascending node is pi / 3, the perigee angle is 0, and the mean anomaly angle is 0. Set the minimum safety distance D between the satellites min =30m. Assume that the initial position and initial velocity of the companion satellite in the x and y directions relative to the leader satellite in the LVLH coordinate system meet the closed elliptical relative motion conditions, but the initial IRE center coordinates of the companion satellite relative to the leader satellite in the xy plane deviate from the origin to varying degrees. In order to evaluate the performance of the algorithm under different conditions, Latin hypercube sampling is used to randomly generate parameters such as the maximum inter-satellite distance, the initial position coordinates of the companion satellite, and the initial IRE center coordinates of the companion satellite. 300 sample examples with different parameter values ​​are obtained, and simulation calculations and statistics are performed. Among them, the initial values ​​of the x, y and z coordinates of the companion satellite in the LVLH coordinate system of the leader satellite are in the range of [-150, 150] m, [-300, 300] m and [-300, 300] m, respectively. The initial IRE center x coordinate and y coordinate ranges are [-60, 60] m and [-180, 180] m, respectively. The maximum inter-satellite distance in the xy plane is D max The value range is [100,200] m. The initial velocity of the companion satellite relative to the leader satellite in the xy plane of the LVLH coordinate system is determined by the closed ellipse relative motion condition, and the initial velocity in the z direction is set to ω times the initial value of the z coordinate.

[0194] To simplify the calculation, Figure 3 For the calculation of the maximum distance control boundary, when the IRE center is located in the second quadrant, the distance from the highest point on the IRE to the origin is approximated as the maximum inter-satellite IRE distance. When the IRE center is located in the fourth quadrant, the distance from the lowest point on the IRE to the origin is approximated as the maximum inter-satellite IRE distance. That is, take The maximum IRE distance at this time is approximately For the calculation of the minimum distance control boundary, the length of the minor semi-axis is AD min, the major semi-axis length is 2A-D min The ellipse is approximated in the first quadrant by Pick up The length of the minor semi-axis is A+D min , the length of the major semi-axis is 2A+D min The ellipse is approximated in the first quadrant by Pick up The above approximation has little error for the problem under consideration, and the companion flight does not require a strict relative motion configuration, so there is no need to calculate these control boundary functions with high precision. In the algorithm implementation, the x-coordinate of the IRE center in the maximum and minimum distance control strategies is preset to an offset of ε x =2m.

[0195] Based on the given initial conditions and algorithm parameters, the relative motion of each sample case is simulated and calculated within 864000s (10 days). In the simulation case, the control conditions are checked, the velocity impulse is calculated and applied at each discrete moment with a fixed time step of 100s. Before the simulation starts, the initial condition of the relative motion of the companion satellite is converted into the initial motion state in the Earth Centered Inertial (ECI) coordinate system. At each discrete impulse calculation moment in the simulation, the instantaneous ECI state of the companion satellite is first converted into the relative motion state in the LVLH coordinate system of the leader satellite, and then the velocity impulse to be applied to the companion satellite is calculated according to the relative motion control strategy, and then the control velocity impulse is converted back to the ECI coordinate system and applied to the companion satellite. In the time period between two adjacent discrete moments, the free orbital motion of each satellite is calculated by numerical integration of the orbital motion model with J2 perturbation. The numerical integration adopts a variable step size algorithm, and the absolute error limit and relative error limit are both set to 1e-10.

[0196] Figure 4 The changes of the normalized intersatellite distance in the xy coordinate plane for 300 sample cases are given. Each curve in the figure represents the change of the normalized intersatellite distance over time for a sample case. The normalization method is to divide the actual intersatellite distance in the xy coordinate plane by the D max The purpose of this figure is to show how well the algorithm satisfies the maximum distance constraint under different parameters. The horizontal dotted line in the figure represents the normalized maximum distance threshold curve, that is, the normalized distance is equal to 1. Figure 5 The actual inter-satellite distance variation over time in the xy coordinate plane of 300 sample cases is given. Each curve in the figure represents the actual inter-satellite distance variation over time of a sample case, and the horizontal dotted line in the figure is the minimum distance threshold. Figure 4 and Figure 5It can be seen that the proposed algorithm can effectively adjust the relative motion of the satellite from the randomly generated initial state to within the set distance range, that is, to achieve long-term control of the relative distance. Figure 4 and Figure 5 The reason why the distance constraint is violated in the initial stage of relative motion control is that the initial state is randomly generated and does not meet the distance range constraint. In the middle and late stages of relative motion control, there will be a slight deviation from the distance range at certain moments. This is due to the existence of perturbations and the approximate simplified calculations in the algorithm implementation, which does not affect the actual application effect of the algorithm.

[0197] The total number of control speed impulses of three different functions (i.e., IRE size adjustment control impulse in the x direction, maximum distance control impulse in the y direction, and minimum distance control impulse in the y direction) calculated by simulation of sample examples, the sum of the absolute values ​​of each impulse of the three different function control impulses, the total number of all control impulses, and the sum of the absolute values ​​of all control impulses are used as statistics. Table 1 gives the speed impulse statistics of distance control within 10 days for 300 sample examples, and gives the maximum value, average value, and sample standard deviation of the corresponding statistics. It can be seen that the speed impulse requirement of the given distance control method is quite small (the maximum value of the total speed impulse within 10 days is only about 0.83m / s, and the average value is about 0.28m / s). The maximum number of impulses required to be implemented by this method within 10 days (about 152 orbital cycles) is 189 times (average 51 times), and the average impulse control needs to be implemented at most about 1.24 times (average about 0.34 times) per orbital cycle, and the required control frequency is also low.

[0198] Table 1 Statistics of control velocity impulse of 300 sample cases

[0199]

[0200] Among the 300 sample examples, two typical sample points are selected and the specific calculation results are given respectively. The parameter values ​​of the two selected typical sample points are shown in Table 2.

[0201] Table 2 Parameter values ​​of two typical sample points selected in the sample example

[0202]

[0203]

[0204] The simulation results of two typical sample points are shown in Figure 6-Figure 13 As shown, Figure 6 and Fig.10 In the figure, the triangle symbols represent the initial relative positions, and the square symbols represent the relative positions at the end of the simulation. Figure 7 and Fig.11The height value and sign represent the magnitude and direction of the impulse respectively. Fig. 9 and Fig.13 The ellipses of different line types represent the ZMDE at the end of the first four impulse controls, the symbols of different shapes mark the IRE center positions before and at the end of the first four impulse controls, and the small dot symbol marks the movement trajectory of the IRE center.

[0205] The embodiment of the present application also provides a distance control system for relative motion between satellites, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the steps of the above method when executing the computer program. The system can implement various embodiments of the distance control method for relative motion between satellites, and can achieve the same beneficial effects, which will not be described in detail here.

[0206] The preferred specific embodiments of the present invention are described in detail above. It should be understood that a person skilled in the art can make many modifications and changes based on the concept of the present invention without creative work. Therefore, any technical solution that can be obtained by a person skilled in the art through logical analysis, reasoning or limited experiments based on the concept of the present invention on the basis of the prior art should be within the scope of protection determined by the claims.

Claims

1. A distance control method for relative motion between satellites, characterized in that: include: Determine a reference satellite and a companion satellite, establish LVLH coordinates with the reference satellite as the center origin, and divide the LVLH coordinate system into U quadrants in a set plane, where U is a positive integer; Determine the instantaneous relative ellipse IRE and the center coordinates (x ct ,y ct ), and according to the center coordinates (x ct ,y ct ) and the positional relationship between the U quadrant areas determine Q first target control areas and W second target control areas, V and W are both positive integers, and the instantaneous relative ellipse IRE is used to represent the motion trajectory between the companion satellite and the reference satellite; reducing the distance between the companion satellite and the reference satellite according to a first positional relationship, wherein the first positional relationship is a positional relationship between the center coordinates of the ellipse IRE and the Q first target control areas; increasing the distance between the companion satellite and the reference satellite according to a second positional relationship, wherein the second positional relationship is a positional relationship between the center coordinates of the ellipse IRE and the W second target control areas; Increasing the distance between the companion satellite and the reference satellite according to the second position relationship comprises: When the center coordinate of the instantaneous relative ellipse IRE is located in the first control area, the x in the center coordinate is adjusted. ct is a first preset value; When the center coordinate of the instantaneous relative ellipse IRE is located in the second control area, the x in the center coordinate is adjusted. ct is a second preset value; The first partial control area is a partial control area of ​​the W second target control areas, and the second partial control area is the remaining control areas of the W second target control areas except the first partial control area; Before reducing the distance between the companion satellite and the reference satellite according to the first position relationship, the method further includes: Determine a first target time period for reducing the distance between the companion satellite and the reference satellite and a second target time period for increasing the distance between the companion satellite and the reference satellite; in the first target time period and the second target time period, a change in the size of the instantaneous relative ellipse IRE caused by adjusting the center coordinates of the instantaneous relative ellipse IRE is within a preset range; The reducing the distance between the companion satellite and the reference satellite according to the first position relationship comprises: reducing the distance between the companion satellite and the reference satellite during the first target time period; The increasing the distance between the companion satellite and the reference satellite according to the second position relationship comprises: The distance between the companion satellite and the reference satellite is increased during the second target time period.

2. The distance control method for relative motion between satellites according to claim 1, characterized in that: The U quadrant regions include a first quadrant region, a second quadrant region, a third quadrant region, and a fourth quadrant region, and reducing the distance between the companion satellite and the reference satellite according to the first position relationship includes: At the instantaneous relative ellipse IRE, the center coordinate is located at x ct ≤0 and y ct ≥y max (x ct ) or in the region of x ct >0 and y ct ≤-y max (-x ct ), adjust the x in the center coordinates ct -x ct ; where y max (x ct ) is the maximum distance boundary function.

3. The distance control method for relative motion between satellites according to claim 1, characterized in that: The W second target control areas include six control areas, namely a first control area, a second control area, a third control area, a fourth control area, a fifth control area and a sixth control area; The starting curve of the first control area is y ct =2A+D min , the termination curve is y ct =2A; The starting curve of the second control area is The termination curve is The starting curve of the third control area is The termination curve is The starting curve of the fourth control area is y ct =-2A-D min , the termination curve is y ct = -2A; The starting curve of the fifth control area is The termination curve is The starting curve of the sixth control area is The termination curve is Where A is the length of the semi-minor axis of IRE, D min Indicates the minimum safe distance between the two stars. represents the function that defines the minimum distance control starting curve outside the ZMDE, represents the function that defines the minimum distance control termination curve outside the ZMDE, represents the function that defines the minimum distance control starting curve within the ZMDE, Represents the curve function that defines the minimum distance control termination within the ZMDE.

4. The distance control method for relative motion between satellites according to claim 3, characterized in that: The increasing the distance between the companion satellite and the reference satellite according to the second position relationship comprises: When the center coordinate of the ellipse IRE is located in any one of the first control area, the third control area or the fifth control area, the x in the center coordinate is adjusted. ct is a first preset value; When the center coordinate of the ellipse IRE is located in any one of the second control area, the fourth control area or the sixth control area, the x in the center coordinate is adjusted. ct is the second preset value.

5. A distance control system for relative motion between satellites, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the computer program, the steps of the method described in any one of claims 1 to 4 are implemented.

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