Space anti-interception observation pose and orbit coupling control method based on escorting small satellite

Abstract

The application relates to a space anti-approaching observation attitude and orbit coupling control method based on a guard satellite, which comprises the following steps: establishing a guard satellite orbit and attitude dynamics model; designing a desired trajectory of the guard satellite in a parent satellite orbit system; designing a desired attitude of the guard satellite; constructing a relative position and attitude coupling dynamics model of the guard satellite relative to the parent satellite according to the guard satellite orbit and attitude dynamics model and the desired attitude; constructing a dynamics model for control input of the relative position and attitude coupling dynamics model characterized by a thruster control force; and constructing an optimal sliding mode attitude and orbit coupling controller of the guard satellite according to the dynamics model for control input characterized by the thruster control force, the desired trajectory, and the like. The method utilizes the advantages of the flexible and light guard satellite, actively adopts an anti-approaching observation strategy of approaching the approaching satellite from the line-of-sight direction of the satellite and interfering with the satellite, and can effectively defend against the approaching satellite approaching and observing the parent satellite.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of computer technology and spacecraft control technology, in particular to a space anti-proximity observation attitude and orbit coupling control method based on a guard satellite. BACKGROUND

[0002] With the development of space technology, space-based situational awareness has become an important way to obtain space target information. Close-range observation based on space-based platforms can obtain important target surface image feature information, which can help analyze its function and technology level, and is an important way of space-based situational awareness. A typical representative is the Geosynchronous Space Situational Awareness Program (GSSAP) satellite, which is constantly approaching some high-value satellites near the geosynchronous orbit to conduct reconnaissance and photography. The orbit and attitude control of active proximity observation and anti-proximity observation between the main and passive spacecraft has become a research hotspot in recent years. In the published literature, the key word is often "orbital game".

[0003] Traditional large spacecraft (hereinafter referred to as mother satellite) has large volume and mass, poor maneuverability, and only relies on its own orbit and attitude maneuvering capability to deal with the proximity observation threat of the incoming satellite, which affects its normal business work and the cost of propellant consumption is high. Carrying a small satellite by the mother satellite and operating it by the small satellite is a promising way of close-range operation, because the small satellite has the advantages of small volume and mass, flexible maneuverability, and low propellant consumption cost. The EAGLE and ROOSTER programs developed by a certain region in recent years have multiple small satellites carried in a mother satellite, which are typical representatives of the mother-daughter operation mode.

[0004] When the incoming satellite approaches the mother satellite for observation, the mother satellite can release a guard satellite carrying interference equipment to actively approach the incoming satellite for interference. During the guard satellite's defense process, the guard satellite needs to quickly and accurately adjust its position and attitude according to the real-time relative state of the incoming satellite and the mother satellite, which directly affects the success or failure of the anti-proximity observation mission. Due to the complex coupling relationship between the orbit and attitude of the guard satellite, orbit and attitude control should be treated as a whole, i.e. an attitude and orbit coupling control method should be used.

[0005] The existing space close approach observation and anti-close approach observation game research mainly focuses on the case of two spacecrafts, and the few game researches involving multiple spacecrafts are mainly the pursuit and evasion game mode of equal spacecrafts, and rarely involve the mode of anti-close approach observation by small satellites in coordination with mother satellites and the corresponding orbit and attitude control method. The control of the guard satellite needs to consider the relative position of the incoming satellite and the mother satellite, and also needs to consider its own orbit and attitude. The existing control method for direct game between mother satellites and incoming satellites is no longer applicable. Therefore, it is necessary to study the space anti-close approach observation orbit and attitude coupling control method based on the guard satellite. SUMMARY

[0006] Therefore, it is necessary to provide a space anti-close approach observation orbit and attitude coupling control method based on a guard satellite in view of the above technical problems.

[0007] A space anti-close approach observation orbit and attitude coupling control method based on a guard satellite, the method comprising:

[0008] Establishing an orbit and attitude dynamics model of the guard satellite.

[0009] Designing a desired trajectory of the guard satellite in the mother satellite orbit system.

[0010] Designing a line-of-sight-constrained guard satellite observation attitude.

[0011] According to the orbit and attitude dynamics model of the guard satellite and the guard satellite observation attitude, a relative position and attitude coupling dynamics model of the guard satellite relative to the mother satellite is constructed.

[0012] According to the relative position and attitude coupling dynamics model of the guard satellite relative to the mother satellite, a dynamics model using thruster control force to represent control input is constructed.

[0013] According to the dynamics model using thruster control force to represent control input and the desired trajectory, an optimal sliding mode orbit and attitude coupling controller of the guard satellite is constructed.

[0014] The aforementioned space-based anti-close-in observation attitude and orbit coupling control method based on escort microsatellites includes: establishing an orbital and attitude dynamic model of the escort microsatellite; designing the desired trajectory of the escort microsatellite in the parent satellite's orbital system; designing the desired attitude of the escort microsatellite with line-of-sight constraints; constructing a coupled dynamic model of the relative position and attitude of the escort microsatellite relative to the parent satellite based on the orbital and attitude dynamic model and the desired attitude of the escort microsatellite; constructing a dynamic model using thruster control force to characterize the control input based on the coupled dynamic model of the relative position and attitude of the escort microsatellite relative to the parent satellite; and constructing an optimal sliding mode attitude and orbit coupling controller for the escort microsatellite based on the dynamic model using thruster control force to characterize the control input and the desired trajectory. This method utilizes the flexibility and portability of escort microsatellites, employing an anti-close-in observation strategy that actively approaches and interferes with the incoming satellite from the line-of-sight direction, effectively defending against incoming satellites conducting close-in observations of our parent satellite. Attached Figure Description

[0015] Figure 1 This is a flowchart illustrating a space-based in-depth observation attitude and orbit coupling control method based on a small satellite in one embodiment.

[0016] Figure 2 This is a schematic diagram of the coordinate system in one embodiment;

[0017] Figure 3 This is a schematic diagram of a task scenario in one embodiment;

[0018] Figure 4 This is a schematic diagram of the thruster arrangement for a small satellite in one embodiment;

[0019] Figure 5 This is a three-dimensional relative motion trajectory of the escort microsatellite in one embodiment;

[0020] Figure 6 This is a distance variation curve between the escorting small satellite and the incoming satellite in one embodiment;

[0021] Figure 7 This is a curve showing the change in the relative position vector angle between the escort satellite and the incoming satellite in one embodiment;

[0022] Figure 8 This is a curve showing the relative position error variation of the escort microsatellite in one embodiment;

[0023] Figure 9 This is a curve showing the relative velocity error variation of the escorting small satellite in one embodiment;

[0024] Figure 10 This is a curve showing the variation of the quaternion error of a small satellite in one embodiment;

[0025] Figure 11This is a thrust variation curve of the escort satellite thruster in one embodiment. Detailed Implementation

[0026] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0027] In one embodiment, such as Figure 1 As shown, a space-based anti-close-range observation attitude and orbit coupling control method based on a small satellite is provided. This method includes the following steps:

[0028] Step 100: Establish the orbital and attitude dynamics model of the escort satellite.

[0029] Specifically, (1) Define the coordinate system. First, establish the geocentric inertial frame O. i X i Y i Z i O, the orbital system of the parent star o X o Y o Z o and spacecraft system O b X b Y b Z b ,like Figure 2 As shown. Geocentric inertial frame O i X i Y i Z i The origin is the Earth's center O. i O i X i The axis lies in the equatorial plane and points towards the vernal equinox, O i Z i The axis aligns with the Earth's rotation axis and points towards the North Pole, O i Y i The axis is determined by the right-hand rule; the parent star orbital system O o X o Y o Z o The origin is the center of mass of the parent star, O. o O o X o The axis is in the same direction as the geocentric radius vector of the parent star, O o Y o The axis lies perpendicular to O in the orbital plane of the parent star. o X o The axis, pointing in the direction of motion, is positive; O o Z o The axis is determined by the right-hand rule; spacecraft system O bX b Y b Z b The origin is the spacecraft's center of mass O. b O b X b O b Y b and O b Z b The axes coincide with the principal axes of inertia of the spacecraft and conform to the right-hand rule.

[0030] (2) Using the parent star's orbital coordinate system as a reference coordinate system, establish a relative orbital dynamics model of the escort satellite relative to the parent star.

[0031] (3) Establish an attitude dynamics model for the escort satellite.

[0032] Step 102: Design the desired trajectory of the escort satellite in the parent satellite's orbital system.

[0033] Step 104: Design the desired attitude of the guardian microsatellite under line-of-sight constraints.

[0034] Step 106: Based on the orbital and attitude dynamics model of the escort satellite and the desired attitude of the escort satellite, construct a coupled dynamics model of the relative position and attitude of the escort satellite relative to the parent satellite.

[0035] Specifically, an attitude-orbit coupling dynamic model considering the unmodeled dynamics of the system and external disturbances was established, and an actuator configuration scheme was designed, which is engineering feasible.

[0036] Step 108: Based on the relative position and attitude coupled dynamic model of the escort satellite relative to the parent satellite, construct a dynamic model that uses thrust control force to characterize the control input.

[0037] Step 110: Based on the dynamic model that uses thrust control force to characterize the control input and the desired trajectory, construct the optimal sliding mode attitude and orbit coupling controller for the escort satellite.

[0038] Specifically, an optimal sliding mode attitude-track coupling controller was designed by combining sliding mode control with optimal control, which increased the robustness and optimality of the controller. At the same time, the hyperbolic tangent function was used to replace the discontinuous sign function, which can effectively reduce the chattering of the controller.

[0039] The aforementioned space-based anti-close-in observation attitude and orbit coupling control method based on escort microsatellites includes: establishing an orbital and attitude dynamic model of the escort microsatellite; designing the desired trajectory of the escort microsatellite in the parent satellite's orbital system; designing the desired attitude of the escort microsatellite with line-of-sight constraints; constructing a relative position and attitude coupling dynamic model of the escort microsatellite relative to the parent satellite based on the orbital and attitude dynamic model and the desired attitude of the escort microsatellite; constructing a dynamic model using thruster control force to characterize the control input based on the relative position and attitude coupling dynamic model of the escort microsatellite relative to the parent satellite; and constructing an optimal sliding mode attitude and orbit coupling controller for the escort microsatellite based on the dynamic model using thruster control force to characterize the control input and the desired trajectory. This method utilizes the advantages of the escort microsatellite's flexibility and light weight, employing an anti-close-in observation strategy that actively approaches and interferes with the incoming satellite from the direction of the incoming satellite's line of sight, effectively defending against incoming satellites conducting close-in observations of our parent satellite.

[0040] In one embodiment, step 100 includes: establishing a linear relative orbital dynamics model of the escort satellite relative to the parent star, using the parent star's orbital coordinate system as a reference coordinate system:

[0041]

[0042] in, x, y, and z are the position coordinates of the escort satellite in the parent star's orbital system, respectively. c =[F cx ,F cy ,F cz ] T F cx F cy and F cz f is the control force acting on the escorting small satellite. d =[f dx ,f dy ,f dz ] T ;f dx f dy and f dz The external unknown bounded disturbance acceleration acting on the escort satellite; m is the mass of the escort satellite; n is the average orbital angular velocity of the parent star.

[0043] Treating the escort microsatellite as a rigid body, the nonlinear dynamic equations of the escort microsatellite's attitude based on error quaternions are established as follows:

[0044]

[0045] Where, q eThe error quaternion of the protective small satellite system relative to the desired system, J is the moment of inertia of the protective small satellite, and T is the number of quaternions. d To protect the small satellite from the unknown bounded disturbance torque, T c To protect the attitude control torque of the small satellite, T g To protect the gravitational gradient torque acting on the small satellite, ω e To protect the angular velocity error of small satellites, q e0 , The error quaternion q are respectively e The target part and the arrow part, To protect the coordinate transformation matrix from the desired system to the system of small satellites, To protect the attitude angular velocity of the small satellite relative to the geocentric inertial frame, To protect the attitude angular acceleration of the small satellite's system relative to the geocentric inertial frame, To protect the attitude angular velocity of the small satellite system relative to the geocentric inertial coordinate system, the superscript "~" indicates the antisymmetric matrix of the vector cross product operation; I 3×3 It is a 3×3 identity matrix.

[0046] Specifically, using the parent star's orbital coordinate system O o X o Y o Z o Using the reference coordinate system, the linear relative orbital dynamics model of the escort satellite with respect to the parent star is expressed as follows:

[0047]

[0048] Where x, y, and z are the position coordinates of the escort satellite in the parent star's orbital system, respectively, and F cx F cy and F cz f is the control force acting on the escorting small satellite. dx f dy and f dz The external unknown bounded disturbance acceleration acting on the escort satellite; m is the mass of the escort satellite, taken as 40 kg; n is the average orbital angular velocity of the parent satellite.

[0049] make According to formula (3), the linear relative orbit dynamics equations shown in formula (1) can be obtained.

[0050] If we consider the escort satellite as a rigid body, then the quaternion-described equations of motion for the escort satellite are:

[0051]

[0052] In the formula, q is the attitude quaternion of the escort satellite system relative to the geocentric inertial frame, ωic is the attitude angular velocity of the escort satellite system relative to the geocentric inertial coordinate system, and the superscript "~" indicates the antisymmetric matrix of the vector cross product operation.

[0053] From the theorem of angular momentum, the attitude dynamics equation of the escort satellite can be obtained as follows:

[0054]

[0055] In the formula, J is the moment of inertia of the escort satellite, and T d To protect the small satellite from the unknown bounded disturbance torque, T c To protect the attitude control torque of the small satellite, T g The gravitational gradient torque that protects the small satellite.

[0056] Let q d To protect the attitude quaternion of the small satellite's desired system relative to the geocentric inertial frame, q e To protect the error quaternion of the small satellite system relative to the desired system, we have:

[0057]

[0058] The coordinate transformation matrix from the desired system to the system for the escorting small satellite is:

[0059]

[0060] Where, q e0 , The error quaternion q are respectively e The target and the vector. Let... To protect the attitude angular velocity of the small satellite relative to the geocentric inertial frame, the angular velocity error ω of the small satellite is... e for:

[0061]

[0062] The nonlinear dynamic equation of the attitude of the escort microsatellite based on the error quaternion is shown in Equation (2).

[0063] In one embodiment, step 102 includes: establishing a coordinate transformation matrix from the incoming satellite system to the parent satellite orbital system; installing the incoming satellite observation instruments on system O. tb X tb If the satellite is aligned with the axis and always pointed towards the center of mass of the parent star, then the desired trajectory of the escorting small satellite will always be within the orbit of the incoming satellite system. tb X tb In the positive axis direction, and using an exponential deceleration method to approach the incoming satellite:

[0064]

[0065] In the formula, R rel (t) and The relative distance and relative velocity between the incoming satellite and the escorting small satellite at time t are given by R. rel (t)=[R rel (0)-r s e at +r s R rel (0) represents the relative distance between the incoming satellite and the escort satellite at the initial moment, a < 0 represents the exponential deceleration coefficient, and r s <R rel The radius of the spherical collision avoidance zone for the incoming satellite.

[0066] Based on the expected relative distance between the escort satellite and the incoming satellite, the expected position of the escort satellite within the incoming satellite system is determined as follows:

[0067]

[0068] in, To protect the small satellite's desired position within the incoming satellite system.

[0069] Based on the expected position of the escort satellite in the incoming satellite system, the coordinate transformation matrix from the incoming satellite system to the parent satellite's orbital system, and the angular velocity of the parent satellite's orbital system relative to the geocentric inertial frame, calculate the expected position and velocity of the escort satellite in the parent satellite's orbital system.

[0070] In one embodiment, the expected position and velocity of the escort satellite in the parent satellite orbital system are calculated based on the expected position of the escort satellite in the incoming satellite system, the coordinate transformation matrix from the incoming satellite system to the parent satellite orbital system, and the angular velocity of the parent satellite orbital system relative to the geocentric inertial frame. This includes: calculating the expected position of the escort satellite in the parent satellite orbital system based on the expected position of the escort satellite in the incoming satellite system and the coordinate transformation matrix from the incoming satellite system to the parent satellite orbital system.

[0071]

[0072] In the formula, The relative position of the incoming satellite within the parent star's orbital system. This is the coordinate transformation matrix from the incoming satellite system to the parent satellite's orbital system.

[0073] Based on the angular velocity of the parent satellite's orbital system relative to the geocentric inertial frame, the coordinate transformation matrix from the incoming satellite system to the parent satellite's orbital system, and the expected position of the escort satellite within the incoming satellite system, calculate the expected velocity and expected acceleration of the escort satellite as described in the parent satellite's orbital system; the expected velocity and expected acceleration of the escort satellite are as follows:

[0074]

[0075]

[0076]

[0077] in, The desired velocity of the escort satellite described in the parent star's orbital system. For the desired acceleration of the escort satellite described in the parent star's orbital system, The angular acceleration of the incoming satellite system relative to the parent star's orbital system. The angular velocity of the incoming satellite system relative to its parent star's orbital system. Let be the angular velocity of the parent star's orbital system relative to the geocentric inertial frame. The angular velocity of the incoming satellite system relative to the Earth's inertial frame. The derivative of the desired position of the small satellite within the incoming satellite system, Let be the derivative of the incoming satellite's relative position within the parent star's orbital system. This is the second derivative of the relative position of the incoming satellite within the parent star's orbital system.

[0078] Specifically, (1) Establish the coordinate transformation matrix from the incoming satellite system to the parent star orbit system.

[0079] When an incoming satellite makes a close-range observation of the parent satellite, the escort satellite must remain on the line connecting the parent satellite and the incoming satellite and approach the incoming satellite as quickly as possible to a relatively close and safe distance. Simultaneously, its jamming equipment must always be pointed at the incoming satellite to effectively interfere with the incoming satellite's observation instruments. Figure 3 As shown. Let and Let be the position and velocity of the parent star in the geocentric inertial frame, respectively. Then, the coordinate transformation matrix from the geocentric inertial frame to the parent star's orbital frame is: in

[0080] Let the attitude transfer matrix of the incoming satellite system from the geocentric inertial frame be... The coordinate transformation matrix from the incoming satellite system to the parent satellite's orbital system. for:

[0081]

[0082] (2) The design takes into account the desired position and relative velocity of the escort satellite in the incoming satellite system, considering both safety and speed.

[0083] Assuming the incoming satellite's observation instruments are always pointed at the parent star's center of mass (the subscript t denotes the incoming satellite), its installation axis is defined as the incoming satellite system O. tb X tb The axis ensures that the desired trajectory of the escorting small satellite remains within the incoming satellite system O. tb X tb In the positive axis direction, and using an exponential deceleration method to approach the incoming satellite:

[0084]

[0085] In the formula, R rel (t) and Let be the relative distance and relative velocity between the incoming satellite and the escorting small satellite at time t, respectively. a < 0 represents the exponential deceleration coefficient, with a value of -0.02. s <R rel The radius of the spherical collision avoidance zone for the incoming satellite is taken as 15m. The expected relative distance R between the escorting small satellite and the incoming satellite. rel (t) is:

[0086] R rel (t)=[R rel (0)-r s e at +r s (17)

[0087] In the formula, R rel (0) represents the relative distance between the incoming satellite and the escorting small satellite at the initial moment, with a value of 180m.

[0088] Therefore, the expected position of the escort satellite in the incoming satellite system is

[0089] (3) Calculate the desired position and velocity of the escort satellite in the parent star's orbital system.

[0090] The desired position of the escort satellite in the parent star's orbital system for:

[0091]

[0092] In the formula, This represents the relative position of the incoming satellite within the parent star's orbital system.

[0093] The angular velocity of the parent star's orbital system relative to the geocentric inertial frame is The angular velocity of the incoming satellite system relative to the geocentric inertial frame is (Available through measurement). Angular velocity of the incoming satellite system relative to the parent star's orbital system. As shown in formula (14).

[0094] Desired velocity of the escorting small satellites described in the parent star's orbital system As shown in formula (12).

[0095] Desired acceleration of the escorting small satellites described in the parent star's orbital system As shown in formula (13).

[0096] In one embodiment, step 104 includes: installing jamming equipment in the small satellite escort system O. cb X cb In the positive direction of the axis, determine the projection of the unit vector of the line-of-sight vector of the escort satellite jamming equipment into the geocentric inertial frame and the escort satellite system; rotate the geocentric inertial frame according to the transformation sequence 3-2 to obtain the escort satellite system, and obtain the coordinate transformation matrix from the escort satellite system to the geocentric inertial frame as follows:

[0097]

[0098] in, To protect the coordinate transformation matrix from the small satellite system to the geocentric inertial frame, the corresponding Euler angles of the geocentric inertial frame rotation according to the transformation sequence in 3-2 are denoted as yaw angle ψ and pitch angle θ, respectively.

[0099] Based on the relationship between the projection of the unit vector of the line-of-sight vector of the escort microsatellite jamming device in the geocentric inertial frame and the escort microsatellite system, and the coordinate transformation matrix from the escort microsatellite system to the geocentric inertial frame, the Euler angles are obtained as follows:

[0100]

[0101] θ=sin -1 (-u iz ) (twenty one)

[0102] Where ψ is the yaw angle and θ is the pitch angle, (u ix ,u iy ,u iz ) is the projection of the unit vector of the line-of-sight vector of the jamming equipment protecting the small satellite onto the x, y, and z axes of the geocentric inertial frame.

[0103] Based on the conversion relationship between Euler angles and quaternions, the desired attitude quaternion q is obtained. d Initial value; assuming the desired angular velocity of the escort satellite is perpendicular to the projection of the unit vector of the line-of-sight vector of the escort satellite's jamming equipment into the geocentric inertial frame, then the desired angular velocity of the escort satellite is:

[0104]

[0105] in, To protect the desired angular velocity of the small satellite, u iTo determine the projection of the unit vector of the line-of-sight vector d of the small satellite jamming equipment in the geocentric inertial frame, These are the derivatives of the positions of the incoming satellite and the escorting small satellite in the geocentric inertial frame, respectively.

[0106] By performing kinematic integration on the attitude motion equations of the escort satellite described by quaternions when the escort satellite is considered as a rigid body, the desired attitude quaternion q is obtained. d .

[0107] Specifically, (1) the design considers the initial values ​​of the Euler angles and quaternions of the desired attitude of the guardian microsatellite under the line-of-sight constraint.

[0108] Assume the jamming equipment is installed in the small satellite protection system O cb X cb In the positive direction of the axis (subscript c indicates the escort satellite), u i and u b Let be the projections of the unit vector d of the line-of-sight vector 'd' of the jamming equipment protecting the small satellite in the geocentric inertial frame and the small satellite system, respectively, with the following expressions:

[0109]

[0110] In the formula, Let be the positions of the incoming satellite and the escort asteroid in the geocentric inertial frame, respectively. Assuming the escort asteroid system is obtained by rotating the geocentric inertial frame according to the rotation sequence in 3-2, and the corresponding Euler angles are denoted as yaw angle ψ and pitch angle θ, then we have... in The expression for the coordinate transformation matrix from the small satellite system to the geocentric inertial frame is shown in formula (19).

[0111] Further analysis revealed:

[0112]

[0113] Let the yaw angle ψ be in the range of [-π, π] with the counterclockwise direction being positive, and the pitch angle θ be in the range of [-π / 2, π / 2] with the counterclockwise direction being positive. Then the Euler angles obtained by inverse solution are shown in formulas (20) and (21).

[0114] Based on the conversion relationship between Euler angles and quaternions (common knowledge in the aerospace field, so I won't elaborate further), the desired attitude quaternion q can be obtained. d Initial value.

[0115] (2) Design consideration of the desired attitude quaternion and angular velocity of the escort microsatellite under line-of-sight constraints.

[0116] Assuming the desired angular velocity of the escort satellite with u i If they are perpendicular, then in the geocentric inertial frame, ui The end-effector velocity is Multiply u on both sides simultaneously to the left i The desired angular velocity can be obtained. for

[0117]

[0118] u based on formula (23) i Differentiation has The expected angular velocity of the escort satellite can be obtained:

[0119]

[0120] Further kinematic integration is performed according to formula (4) (common knowledge in the aerospace field, and will not be elaborated further) to obtain the desired attitude quaternion q. d .

[0121] In one embodiment, step 106 includes: constructing a coupled dynamic model of the relative position and attitude of the escort satellite relative to the parent satellite based on the escort satellite's orbital and attitude dynamics model and the escort satellite's desired attitude.

[0122]

[0123] In the formula, u is the control input. F c T is the control force acting on the small satellite. c To protect the attitude control torque of the small satellite, f d T represents the external, unknown, bounded interference acceleration acting on the escorting small satellite. d The unknown bounded disturbance torque experienced by the small satellite, Δ∈R 7×7 For the unmodeled dynamics of the system, D1, D2, and D3 are three matrices constructed from the coefficients of the attitude dynamics model of the escort microsatellite.

[0124] Specifically, a coupled dynamics model of the relative position and attitude of the escort satellite is constructed. State variables are defined. Considering the unmodeled dynamics of the system, the coupled dynamic model of the relative position and attitude of the escort satellite relative to the parent satellite, as shown in Equation (27), is obtained from Equations (1) and (2).

[0125] In one embodiment, step 108 includes: characterizing the control input in the coupled dynamics model of the relative position and attitude of the escort microsatellite using thruster control forces as follows:

[0126]

[0127] Where f is the thrust vector of the thruster, f = [f1, f2, f3, f4, f5, f6] T D4 is the input matrix for the thruster configuration.

[0128] Based on the relative position and attitude coupled dynamics model of the escort satellite relative to the parent satellite and the control input represented by thruster control force, the dynamics model representing the control input using thruster control force is obtained as follows:

[0129]

[0130] In the formula, D2 is a matrix constructed from the coefficients of the attitude dynamics model of the escort satellite.

[0131] Specifically, six bidirectional thrusters are selected as the attitude and orbit control actuators for the escort microsatellite. The escort microsatellite is approximated as an L×L×L cube, where L is 1m. The thrusters are configured as follows: Figure 4 As shown. Then the control input u is:

[0132]

[0133] Where f is the thrust vector of the thruster, f = [f1, f2, f3, f4, f5, f6] T The input matrix D4 for the thruster configuration is:

[0134]

[0135] Substituting formula (30) into formula (27) yields the dynamic model shown in formula (29), which uses the thruster control force to characterize the control input.

[0136] In one embodiment, step 110 includes: based on the dynamic model that uses thrust control force to characterize the control input, constructing the basic form of the satellite attitude-orbit coupling controller using a sliding mode control method, as follows:

[0137]

[0138] Where λ is a seventh-order positive definite diagonal matrix, σ∈R 7×1 As an auxiliary parameter, e is the error vector for the attitude and orbit coupling control of the escort satellite. To protect the first derivative of the error vector of the small satellite's attitude and orbit coupling control, The second derivative of the error vector for the attitude and orbit coupling control of the small satellite.

[0139] Based on the basic form of the attitude and orbit coupling controller for the escort microsatellite, the optimal sliding mode attitude and orbit coupling control law for the escort microsatellite is constructed using optimal control theory.

[0140] By replacing the sign function with the hyperbolic tangent function, the chattering of the optimal sliding mode attitude and orbit coupling controller is reduced, and the optimal sliding mode attitude and orbit coupling control law of the escort small satellite based on the hyperbolic tangent function is obtained.

[0141] Specifically, for the dynamic model shown in formula (29) that uses thrust control force to characterize the control input, an optimal sliding mode control method is used to design the attitude and orbit coupling controller for the escort microsatellite. The error vector of the escort microsatellite attitude and orbit coupling control is defined as... The first derivative of the error vector is make The second derivative of the error vector is:

[0142]

[0143] Define the sliding mode function as follows:

[0144]

[0145] In the formula, λ is a seventh-order positive definite diagonal matrix, with values ​​of λ = diag(0.02, 0.02, 0.02, 0.1, 0.1, 0.1, 0.1); σ ∈ R 7×1 These are auxiliary parameters that will be used to design the optimal control law.

[0146] Define the following Lyapunov function:

[0147]

[0148] but:

[0149]

[0150] To ensure Design the following control law:

[0151]

[0152] In the formula, D -1 Let D be the generalized inverse matrix of D. -1 =(D T D) -1 D T ε is a seventh-order positive definite diagonal matrix with the value ε = diag(1,1,1,1,1,1,1,1), and sgn(s) is the sign function. Substituting formula (37) into formula (36) yields:

[0153]

[0154] In the formula, if we take |ε|≥|D3d+Δ|, then we have That is, the system is globally asymptotically stable under the action of formula (37). At this time, in formula (37) For parameters to be determined, once determined... This will give you the complete control law.

[0155] Substituting formula (37) into formula (33) yields:

[0156]

[0157] Since εsgn(s) can handle external disturbances and system uncertainties, formula (39) can be approximately expressed as formula (32).

[0158] In one embodiment, based on the basic form of the escort microsatellite attitude-orbit coupling controller, the optimal sliding mode attitude-orbit coupling control law for the escort microsatellite is constructed using optimal control theory as follows:

[0159]

[0160] Among them, B op All are constant matrices. P(X op Let ) be a solution to the Riccati equation, ε be a seventh-order positive definite diagonal matrix, and s be the sliding mode function. sgn(·) is the sign function. The desired velocity of the escort satellite described in the parent star's orbital system.

[0161] Specifically, the system state variable is selected as And order The original system then transforms into:

[0162]

[0163] In the formula,

[0164] The controllability matrix of the system described by formula (41) is:

[0165]

[0166] Since λ is a positive definite diagonal matrix, it is easy to know that M is a full-rank matrix. Therefore, the system described by equation (41) is controllable, and the optimal control law can be designed with the help of optimal control theory.

[0167] Consider the following performance metric function:

[0168]

[0169] Where Q is a 14th-order symmetric positive semi-definite matrix and R is a 7th-order symmetric positive definite matrix. Therefore, the optimal control problem of the system described by formula (41) can be described as: designing a feedback control law U op While satisfying formula (41), the performance index described by formula (43) is minimized.

[0170] Referring to the linear quadratic regulator (LQR) algorithm, the optimal feedback control law is selected as follows:

[0171]

[0172] Wherein, P(X) op () is a solution to the following Riccati equation:

[0173]

[0174] To satisfy the optimality condition, the following must be met:

[0175]

[0176] Therefore, when P(X) op When ) is a constant value, the control law U described by formula (44) op If the feedback is optimal, it is a suboptimal feedback control law; otherwise, it is a suboptimal feedback control law. The value of is used as an evaluation index for optimality. As it gets closer to 0, the control law U... op The closer to optimal feedback control, the better. Because A op B op Both are constant matrices. From formula (45), it can be seen that when Q and R are both constant matrices, the solved P(X) op ) is a constant value, that is This leads to the optimal feedback control law U. op Relevant parameter settings: R = I 7×7 Q = diag(1,1,1,10) -7 10 -7 10 -7 10 -7 10 -7 10 -7 10 -7 10 -7 10 -7 10 -7 10 -7 ).

[0177] Combining formulas (37) and (44), we can obtain the optimal sliding mode control law for the escort satellite as shown in formula (40).

[0178] In one embodiment, the method further includes: replacing the sign function with a hyperbolic tangent function to reduce chattering in the optimal sliding mode attitude and orbit coupling control law of the escort microsatellite; wherein the optimal sliding mode attitude and orbit coupling control law of the escort microsatellite based on the hyperbolic tangent function is:

[0179]

[0180] Where tanh(·) is the hyperbolic tangent function, and p is the transfer factor that satisfies p>0.

[0181] Specifically, the hyperbolic tangent function is used instead of the sign function to reduce chattering in the optimal sliding mode attitude-orbit coupling controller. The hyperbolic tangent function tanh(·) is used instead of the sign function sgn(·) in formula (40), where p is the transfer factor and satisfies p>0. The value of p is 1, and the optimal sliding mode control law of the escort small satellite based on the hyperbolic tangent function is obtained as shown in formula (47).

[0182] It should be understood that, although Figure 1 The steps in the flowchart are shown sequentially as indicated by the arrows, but these steps are not necessarily executed in the order indicated by the arrows. Unless otherwise specified herein, there is no strict order in which these steps are executed, and they can be performed in other orders. Figure 1 At least some of the steps in the process may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily completed at the same time, but can be executed at different times. The execution order of these sub-steps or stages is not necessarily sequential, but can be executed in turn or alternately with other steps or at least some of the sub-steps or stages of other steps.

[0183] In the verification embodiment, it is assumed that the initial orbital root numbers of the parent star are a = 42235590m, e = 0.000528, i = 8.40°, Ω = 51.33°, ω = -122.19°, and f = 0.49°, and the orbital integral takes into account the perturbation effect of the J2 term.

[0184] Let the moment of inertia matrix of the escort satellite be J = diag(5,5,5) kg·m 2 A single thruster can generate a maximum thrust of 5 N. The initial position of the escort satellite is [13, 1, -13]. T m, initial velocity [1, 1, -1] T m / s, initial quaternion is [1,0,0,0] T The initial attitude angular velocity is [0.001, 0.001, 0.001]. Trad / s. The simulation time is set to 1000s, with a step size of 0.1s. During the relatively short flight time, the mass and moment of inertia of the escort satellite can be approximated as constant. Considering that the unmodeled dynamics can be equivalent to interference, the interference acceleration and torque in the simulation are magnified by a factor of 10, expressed as:

[0185] f d = 10 × [1.0, -2.0, -1.0] T sin(0.02t)×10 -5 m / s 2

[0186] T d = 10 × [2.0, -1.0, 1.5] T sin(0.04t)×10 -4 N·m

[0187] Simulation results of the attitude and orbit coupling control method based on the anti-close observation of the escort microsatellite are shown in Figure 5- Figure 11 As shown in the figure, the escort satellite approaches the incoming satellite to a position approximately 15 meters away within 200 seconds along the line of sight, and then maintains this distance. The convergence time for the escort satellite's relative position and velocity is approximately 45 seconds, and the convergence time for the error quaternion is approximately 70 seconds. Due to the large initial deviation, the thrust of the escort satellite's thrusters saturates, but as the deviation decreases, the thrust rapidly decreases and remains at a relatively small value.

[0188] Simulation results show that the escort satellite effectively reached the desired position to interfere with the incoming satellite, successfully protecting the mother satellite from close-range observation by the incoming satellite.

[0189] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0190] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this application should be determined by the appended claims.

Claims

1. A space-based indirect observation attitude and orbit coupling control method based on a satellite escort microsatellite, characterized in that, The method includes: Establish a dynamic model of the orbit and attitude of the escort satellite; Design the desired trajectory of the escort satellite in the parent star's orbital system; Design the desired attitude of the guardian microsatellite under line-of-sight constraints; Based on the orbital and attitude dynamics model of the escort satellite and the desired attitude of the escort satellite, the coupled dynamics model of the relative position and attitude of the escort satellite relative to the parent satellite is constructed as follows: in, , , u To control the input, , For the control force acting on the small satellite, To protect the attitude control torque of the small satellite, , For the external unknown bounded interference acceleration acting on the escort satellite, To protect the small satellite from the unknown bounded disturbance torque, For systems without modeled dynamics, These are three matrices constructed from the coefficients of the escort satellite attitude dynamics model; Based on the relative position and attitude coupled dynamics model of the escort satellite relative to the parent satellite, a dynamics model is constructed that uses thrust control force to characterize the control input; Based on the dynamic model that uses thrust control force to characterize the control input and the desired trajectory, an optimal sliding mode attitude-orbit coupling controller for the escort satellite is constructed.

2. The method according to claim 1, characterized in that, Establish a dynamic model of the satellite's orbit and attitude, including: Using the parent star's orbital coordinate system as the reference coordinate system, the linear relative orbital dynamics model of the escort satellite relative to the parent star is established as follows: in, , x , y and z These are the position coordinates of the escort satellite within the parent star's orbital system. , , and For the control force acting on the small satellite, ; , and This refers to the external, unknown, bounded interference acceleration acting on the escort satellite; m To protect the quality of small satellites; , , n The average orbital angular velocity of the parent star; Treating the escort microsatellite as a rigid body, the nonlinear dynamic equations of the escort microsatellite's attitude based on error quaternions are established as follows: in, To protect the error quaternion of the small satellite system relative to the desired system, J To protect the rotational inertia of the small satellite, T d To protect the small satellite from the unknown bounded disturbance torque, T c To protect the attitude control torque of the small satellite, To protect the gravitational gradient torque acting on the small satellite, , , , , To protect the angular velocity error of small satellites, , These are the error quaternions. The target part and the arrow part, To protect the coordinate transformation matrix from the desired system to the system of small satellites, , To protect the attitude angular velocity of the small satellite relative to the geocentric inertial frame, To protect the attitude angular acceleration of the small satellite's system relative to the geocentric inertial frame, To protect the attitude angular velocity of the small satellite system relative to the geocentric inertial coordinate system, the superscript "~" indicates the antisymmetric matrix of the vector cross product operation; It is a 3×3 identity matrix.

3. The method according to claim 1, characterized in that, Design the desired trajectory of the escort satellite within the parent satellite's orbital system, including: Establish a coordinate transformation matrix from the incoming satellite system to the parent satellite's orbital system; The incoming satellite observation instruments are always pointed at the center of mass of the parent star, and their mounting axis is defined as the incoming satellite system. O tb X tb The axis ensures that the desired trajectory of the escorting small satellite remains within the incoming satellite system. O tb X tb In the positive axis direction, and using an exponential deceleration method to approach the incoming satellite: In the formula, and They are respectively t The relative distance and relative speed between the attacking satellite and its escorting microsatellites are imminent. , R rel (0) represents the relative distance between the incoming satellite and the escorting small satellite at the initial moment. The deceleration coefficient is exponential. The radius of the spherical collision avoidance zone for the incoming satellite; Based on the expected relative distance between the escort satellite and the incoming satellite, the expected position of the escort satellite within the incoming satellite system is determined as follows: in, To protect the small satellite's desired position within the incoming satellite system; Based on the expected position of the escort satellite in the incoming satellite system, the coordinate transformation matrix from the incoming satellite system to the parent satellite's orbital system, and the angular velocity of the parent satellite's orbital system relative to the geocentric inertial frame, calculate the expected position and velocity of the escort satellite in the parent satellite's orbital system.

4. The method according to claim 3, characterized in that, Based on the desired position of the escort satellite within the incoming satellite system, the coordinate transformation matrix from the incoming satellite system to the parent satellite's orbital system, and the angular velocity of the parent satellite's orbital system relative to the geocentric inertial frame, calculate the desired position and velocity of the escort satellite within the parent satellite's orbital system, including: Based on the expected position of the escort satellite in the incoming satellite system and the coordinate transformation matrix from the incoming satellite system to the parent satellite's orbital system, the expected position of the escort satellite in the parent satellite's orbital system is calculated as follows: In the formula, The relative position of the incoming satellite within the parent star's orbital system. This is the coordinate transformation matrix from the incoming satellite system to the parent satellite's orbital system; Based on the angular velocity of the parent satellite's orbital system relative to the geocentric inertial frame, the coordinate transformation matrix from the incoming satellite system to the parent satellite's orbital system, and the expected position of the escort satellite within the incoming satellite system, the expected velocity and expected acceleration of the escort satellite described in the parent satellite's orbital system are calculated; the expected velocity and expected acceleration of the escort satellite are as follows: in, The expected velocity of the escort satellites described in the parent star's orbital system. For the desired acceleration of the escort satellite described in the parent star's orbital system, The angular acceleration of the incoming satellite system relative to the parent star's orbital system. The angular velocity of the incoming satellite system relative to its parent star's orbital system. Let be the angular velocity of the parent star's orbital system relative to the geocentric inertial frame. The angular velocity of the incoming satellite system relative to the Earth's inertial frame. The derivative of the desired position of the small satellite within the incoming satellite system, Let be the derivative of the incoming satellite's relative position within the parent star's orbital system. This is the second derivative of the relative position of the incoming satellite within the parent star's orbital system.

5. The method according to claim 1, characterized in that, Design the desired attitude of the guardian small satellite under line-of-sight constraints, including: Install jamming equipment in the small satellite protection system O cb X cb In the positive direction of the axis, the projection of the unit vector of the line-of-sight vector of the escort microsatellite jamming equipment in the geocentric inertial frame and the escort microsatellite system; Rotating the geocentric inertial frame according to the transformation sequence 3-2 yields the escort satellite system. The coordinate transformation matrix from the escort satellite system to the geocentric inertial frame is: in, To protect the coordinate transformation matrix from the small satellite system to the geocentric inertial frame, the Euler angles corresponding to the rotation of the geocentric inertial frame according to the transformation order in 3-2 are denoted as yaw angles. Pitch angle ; Based on the relationship between the projection of the unit vector of the line-of-sight vector of the escort microsatellite jamming device in the geocentric inertial frame and the escort microsatellite system, and the coordinate transformation matrix from the escort microsatellite system to the geocentric inertial frame, the Euler angles are obtained as follows: in, For yaw angle, The pitch angle, The unit vector of the line-of-sight vector of the small satellite jamming equipment in the geocentric inertial frame. x, y, z Projection of the axis; Based on the conversion relationship between Euler angles and quaternions, the desired pose quaternion is obtained. Initial value; If the desired angular velocity of the escort satellite is perpendicular to the projection of the unit vector of the line-of-sight vector of the escort satellite's jamming equipment into the geocentric inertial frame, then the desired angular velocity of the escort satellite is: in, To protect the expected angular velocity of the small satellite, To protect the line-of-sight vector of small satellite jamming equipment d The projection of the unit vector in the geocentric inertial frame. , These are the derivatives of the positions of the incoming satellite and the escorting small satellite in the geocentric inertial frame, respectively. By performing kinematic integration on the attitude motion equations of the escort microsatellite described by quaternions when the microsatellite is treated as a rigid body, the desired attitude quaternions are obtained. .

6. The method according to claim 1, characterized in that, Based on the coupled dynamics model of the relative position and attitude of the escort satellite relative to the parent satellite, a dynamics model is constructed that uses thrust control force to characterize the control input, including: The control input in the coupled dynamic model of the relative position and attitude of the escort satellite is characterized by the thruster control force: in, f For thruster thrust, , D 4 represents the input matrix configured for the thruster. Based on the relative position of the escort satellite to the parent satellite, the attitude coupling dynamics model, and the control input represented by thruster control force, the dynamics model representing the control input using thruster control force is obtained as follows: In the formula, , This is a matrix constructed from the coefficients of the attitude dynamics model of the escort satellite.

7. The method according to claim 1, characterized in that, Based on the dynamic model that uses thrust control force to characterize the control input and the desired trajectory, an optimal sliding mode attitude-orbit coupling controller for the escort small satellite is constructed, including: Based on the dynamic model that uses thrust control force to characterize the control input, the basic form of the attitude and orbit coupling controller for the escort small satellite is constructed using the sliding mode control method as follows: in, It is a 7th order positive definite diagonal matrix. As auxiliary parameters, To protect the error vector of the small satellite's attitude and orbit coupling control, To protect the first derivative of the error vector of the small satellite's attitude and orbit coupling control, The second derivative of the error vector for the attitude and orbit coupling control of the small satellite; Based on the basic form of the attitude and orbit coupling controller for the escort microsatellite, the optimal sliding mode attitude and orbit coupling control law for the escort microsatellite is constructed using optimal control theory. By replacing the sign function with the hyperbolic tangent function, the chattering of the optimal sliding mode attitude and orbit coupling controller is reduced, and the optimal sliding mode attitude and orbit coupling control law of the escort small satellite based on the hyperbolic tangent function is obtained.

8. The method according to claim 7, characterized in that, Based on the basic form of the attitude-orbit coupling controller for the escort microsatellite, the optimal sliding mode attitude-orbit coupling control law for the escort microsatellite is constructed using optimal control theory as follows: in, B op All are constant matrices. , P ( X op ) represents a solution to the Riccati equation. ε It is a 7th order positive definite diagonal matrix. For sliding mode function, , For symbolic functions, , The desired velocity of the escort satellite described in the parent star's orbital system.

9. The method according to claim 8, characterized in that, The method further includes: replacing the sign function with a hyperbolic tangent function to reduce chattering in the optimal sliding mode attitude and orbit coupling control law of the escort microsatellite; wherein the optimal sliding mode attitude and orbit coupling control law of the escort microsatellite based on the hyperbolic tangent function is: in, It is the hyperbolic tangent function. p It is a transfer factor and satisfies p >0.

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