A method for service spacecraft hovering control

Abstract

The application discloses a kind of service spacecraft hovering control methods, comprising: establishing spacecraft relative motion equation, specific steps include: establishing track relative motion model;According to the track relative motion model, the dynamic model of target star and service spacecraft is established respectively;Through establishing the relative position vector of the service spacecraft and the target star, the track motion equation of the service spacecraft relative to the target star is obtained;Through setting the position error vector of the service spacecraft, the final spacecraft relative motion equation is obtained according to the track motion equation;According to the spacecraft relative motion equation, a closed-loop controller is designed, and a continuous control force is applied to the service spacecraft according to the closed-loop controller, so that the service spacecraft hovers relative to the target star.The method of the application can be realized in engineering in a limited time for the service spacecraft to hover on the specified target star, and has great use value.

Description

Technical Field

[0001] This invention relates to the field of spacecraft control technology, and more specifically to a hovering control method for service spacecraft. Background Technology

[0002] With enhanced ground-based telemetry and control capabilities, improved space-based target identification, space operations, and orbital maneuvering capabilities, hovering technology relative to space targets will become an important development direction for future space applications, playing a crucial role in on-orbit maintenance, photographic observation, and rendezvous and docking. Spacecraft hovering refers to maintaining the position of a service satellite relative to a target satellite using specific methods. In the target satellite's orbital coordinate system (not its inertial coordinate system), the service satellite appears to be at a fixed point relative to the target satellite. The spacecraft used for "hovering" is typically called the service satellite, and the tracked object is called the target satellite. If the target satellite is in a circular orbit, the simplest hovering method is to align the service satellite with the target satellite using the same orbital plane, altitude, and velocity, and to have the service satellite lead or lag behind the target satellite by a phase angle. This achieves hovering without requiring control of the service satellite. Apart from this method, hovering cannot be achieved without control. Generally, service satellites that perform specific functions are in non-Kepler orbits. Hovering cannot usually be achieved by designing orbital parameters alone. Therefore, a finite-time hovering control strategy that can be implemented in engineering is needed and has great practical value. Summary of the Invention

[0003] To address the aforementioned problems, this invention provides a hovering control method for servicing spacecraft, which enables servicing spacecraft to hover over a designated target satellite within a limited time.

[0004] The technical solution of the present invention is as follows:

[0005] A hovering control method for a servicing spacecraft includes the following steps:

[0006] The specific steps for establishing the relative motion equations of a spacecraft include:

[0007] Establish a model of relative orbital motion;

[0008] Based on the orbital relative motion model, dynamic models of the target satellite and service spacecraft are established respectively.

[0009] The orbital motion equation of the service spacecraft relative to the target star is obtained by establishing the relative position vector between the service spacecraft and the target star;

[0010] By establishing the target star's position error vector, the final spacecraft relative motion equation is obtained based on the orbital motion equation.

[0011] A closed-loop controller is designed based on the relative motion equations of the spacecraft. The closed-loop controller applies continuous control force to the service spacecraft to achieve hovering of the service spacecraft relative to the target star.

[0012] A further technical solution of the present invention is: the target star dynamics model is:

[0013]

[0014] The dynamic model of the service spacecraft is as follows:

[0015]

[0016] Where, μ e r is the Earth's gravitational constant. t r represents the distance from the Earth's center to the target star. t =||r t ||,d t The m represents the external perturbation force acting on the target star. t The mass r of the target star is indicated by the mass of the target star. c r represents the distance from the Earth's center to the service spacecraft. c =||r c ||,d c The m represents the external perturbation force experienced by the servicing spacecraft. c Indicates the mass of the service spacecraft, u c For active control forces acting on service spacecraft.

[0017] A further technical solution of the present invention is: obtaining the orbital motion equation of the service spacecraft relative to the target star by establishing the relative position vector between the service spacecraft and the target star, specifically including:

[0018] Let the relative position vector be Then, from the target star dynamics model formula and the service spacecraft dynamics model formula, we obtain...

[0019]

[0020] make In the target star orbital coordinate system F o The coordinates below are represented as ρ = [x, y, z]. T r t In F o The coordinates below are represented as Then r c In F o The coordinate system is represented as follows: And the distance from the Earth's center

[0021] Where d cand d t These represent the external disturbance torques experienced by the service spacecraft and the target satellite, respectively. c Indicates the quality of the serviced spacecraft. c It refers to the control force applied to the service spacecraft.

[0022] make and u c In F o The coordinates in the system are d and u, respectively. According to the relative differentiation formula, both sides of equation (3) are projected onto F. o Tie down, get

[0023]

[0024] The target star's orbital angular velocity is angular acceleration is θ t The true perimeter angle of the target star;

[0025] in

[0026]

[0027]

[0028] Expanding equation (4), we obtain the orbital motion equation of the service spacecraft relative to the target star as follows:

[0029]

[0030] in in Let a be the average angular velocity of the target star. t and e t These are the semi-major axis and eccentricity of the target star's orbit, respectively. 3×3 This represents a third-order identity matrix.

[0031] A further technical solution of the present invention is: by establishing the position error vector of the service spacecraft, the final relative motion equation of the spacecraft is obtained according to the orbital motion equation, specifically including:

[0032] Let the desired position error and velocity error be ρ d , Let the error vector be e = ρ - ρ d Then, rewriting equation (5) yields the final equation of relative motion for the spacecraft:

[0033]

[0034] in

[0035] A further technical solution of the present invention is: designing a closed-loop controller based on the spacecraft's relative motion equations, wherein the closed-loop controller is:

[0036]

[0037]

[0038] Where k i (i = 1, 2, 3, 4) are constants;

[0039] Suppose v(t) is a continuously differentiable positive definite function that satisfies

[0040]

[0041] Where a > 0, b > 0, 0 < ξ < 1, then the system will complete the process in a finite time t. f Converging to equilibrium point

[0042]

[0043] A fast nonsingular sliding surface is presented based on the MSTSM method:

[0044]

[0045]

[0046] Where f(e) = [f(e1), f(e2), f(e3)], r1 = (2-γ)η γ-1 r2=(γ-1)η γ-2 ,0<γ<1,sig(e i ) γ =sign(e i )|e i | γ ,α,β,λ,η are positive constants.

[0047] The present invention provides a hovering control method for servicing spacecraft, which addresses the situation where current servicing spacecraft are in non-Kepler orbits, making hovering impossible based solely on orbital parameter design. The proposed method is a finite-time control strategy that can be implemented in engineering, enabling servicing spacecraft to hover over a designated target satellite within a finite time, and has significant practical value. Attached Figure Description

[0048] Figure 1 This is a schematic diagram of the hovering control method for service spacecraft in an embodiment of the present invention;

[0049] Figure 2This is a schematic diagram of the method for establishing the relative motion equations of a spacecraft in an embodiment of the present invention;

[0050] Figure 3 This is a schematic diagram of the orbital relative motion model established in an embodiment of the present invention;

[0051] Figure 4 This is a schematic diagram of the relative displacement error curve in an embodiment of the present invention;

[0052] Figure 5 This is a schematic diagram of the relative velocity error curve in an embodiment of the present invention;

[0053] Figure 6 This is a schematic diagram of the hovering position curve in an embodiment of the present invention;

[0054] Figure 7 This is a schematic diagram of the control force curve in an embodiment of the present invention. Detailed Implementation

[0055] The present invention will now be described in further detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are for illustrative purposes only and are not intended to limit the scope of the invention. Furthermore, it should be noted that, for ease of description, only the parts relevant to the present invention are shown in the drawings, not the entire structure.

[0056] Before discussing the exemplary embodiments in more detail, it should be noted that some exemplary embodiments are described as processes or methods depicted as flowcharts. Although the flowcharts describe the steps as sequential processes, many of these steps can be performed in parallel, concurrently, or simultaneously. Furthermore, the order of the steps can be rearranged. The process can be terminated when its operation is complete, but may also have additional steps not included in the figures. The process can correspond to a method, function, procedure, subroutine, subroutine, etc.

[0057] One embodiment of the hovering control method for a servicing spacecraft, see [link / reference]. Figure 1 This includes the following steps:

[0058] Step 1: Establish the equations of relative motion for the spacecraft. (See [link]) Figure 2 The specific steps include:

[0059] Step 11: Establish a model of relative orbital motion;

[0060] In the specific implementation process, see Figure 3 Establish a model of relative orbital motion, where F I For the equatorial inertial coordinate system (O I X I Y I Z I Its origin O IFor the Earth's core; X I The axis lies in the equatorial plane and points towards the vernal equinox; Z I The axis is along the direction of the Earth's rotation axis, with upward being positive; Y I Axis and X I Axis and Z I The axes form a right-handed rectangular coordinate system. F o For the target star's orbital coordinate system (o o x o y o z o The coordinate system serves as the reference coordinate system for the relative motion of the spacecraft, with the fundamental plane being the instantaneous orbital plane of the satellite and the origin at o. o At the satellite's center of mass, z o The axis points from the satellite's center of mass to the Earth's center, y o The axis perpendicular to the instantaneous orbital plane points in the direction of the negative normal to the satellite's orbital plane, x. o The axis forms a right-handed coordinate system with the other two axes.

[0061] Step 12: Establish dynamic models of the target satellite and service spacecraft based on the orbital relative motion model.

[0062] In the specific implementation process, assuming that the target star is not subject to active control, its dynamic model is as follows:

[0063]

[0064] The dynamic model of the service spacecraft is as follows:

[0065]

[0066] Where, μ e r is the Earth's gravitational constant. t r represents the distance from the Earth's center to the target star. t =||r t ||,d t The m represents the external perturbation force acting on the target star. t The mass of the target star, r c r represents the distance from the Earth's center to the service spacecraft. c =||r c ||,d c The m represents the external perturbation force experienced by the servicing spacecraft. c Indicates the quality of the service spacecraft, u c For active control forces acting on service spacecraft.

[0067] Step 13: Obtain the orbital motion equation of the service spacecraft relative to the target star by establishing the relative position vector between the service spacecraft and the target star;

[0068] In the specific implementation process, let the relative position vector be... Then, from the target star dynamics model formula and the service spacecraft dynamics model formula, we obtain...

[0069]

[0070] make In the target star orbital coordinate system F o The coordinates below are represented as ρ = [x, y, z]. T r t In F o The coordinates below are represented as Then r c In F o The coordinate system is represented as follows: And the distance from the Earth's center Here, ρ is a coordinate system with the target star as the origin and the line connecting the Earth's center and the target star as the z-axis. Therefore, r t The coordinate representation is and This represents the coordinates of the target star in a coordinate system with the service spacecraft as the origin. Therefore, the service spacecraft's coordinates in the target star's orbital coordinate system F... o The coordinates below are

[0071] make and f c In F o The coordinates in the system are d and u, respectively. According to the relative differentiation formula, both sides of equation (3) are projected onto F. o Tie down, get

[0072]

[0073] The target star's orbital angular velocity is angular acceleration is θ t The true perimeter angle of the target star;

[0074] in

[0075]

[0076]

[0077] Expanding equation (4), we obtain the orbital motion equation of the service spacecraft relative to the target star as follows:

[0078]

[0079] in in Let a be the average angular velocity of the target star. t and e t These are the semi-major axis and eccentricity of the target star's orbit, respectively. 3×3 This represents a third-order identity matrix.

[0080] Step 14: By establishing the position error vector of the service spacecraft, the final relative motion equation of the spacecraft is obtained according to the orbital motion equation;

[0081] In the specific implementation process, let the desired position and velocity be ρ. d , Let the error vector be e = ρ - ρ d Then, rewriting equation (5) yields the final equation of relative motion for the spacecraft:

[0082]

[0083] in

[0084] Step 2: Design a closed-loop controller based on the relative motion equation of the spacecraft, and apply continuous control force to the service spacecraft according to the closed-loop controller to achieve hovering of the service spacecraft relative to the target star.

[0085] In the specific implementation process, a closed-loop controller is designed based on the spacecraft's relative motion equations. The closed-loop controller is as follows:

[0086]

[0087]

[0088] Where k i (i = 1, 2, 3, 4) are constants;

[0089] Suppose v(t) is a continuously differentiable positive definite function that satisfies

[0090]

[0091] Where a > 0, b > 0, 0 < ξ < 1, then the system will complete the process in a finite time t. f Converging to equilibrium point

[0092]

[0093] A fast nonsingular sliding surface is presented based on the MSTSM method:

[0094]

[0095]

[0096] Where f(e) = [f(e1), f(e2), f(e3)], r1 = (2-γ)η γ-1 r2=(γ-1)η γ-2 ,0<γ<1,sig(e i ) γ =sign(e i )|e i | γ ,α,β,λ,η are positive constants.

[0097] To better demonstrate the effects of the present invention, a specific example is provided in the embodiment. The spacecraft parameters used in the example include: the mass of the target satellite is 5079 kg, the mass of the service spacecraft is 200 kg, and the moment of inertia of the target satellite is...

[0098]

[0099] Assuming the target star is in geostationary orbit, the initial orbital parameters are: orbital radius a = 4.2164 × 10⁻⁶. 7 m, eccentricity e=0, right ascension of ascending node Ω=0, orbital inclination i=0, perigee argument ω=0, true perigee angle f=0. For orbital perturbation, consider the situation where the target star and service spacecraft are mainly subjected to gravitational perturbations of terms J2~J4 and measurement errors. Assuming the position measurement deviation is 5m and the velocity measurement deviation is 0, the parameters of the controller equation (7)-(8) are selected as follows: k1=0.0007, k2=0.0003, k3=0.00005, k4=0.00001, α=0.00001, β=0.00001, γ=0.69, η=0.0001. The hovering position is r d = [-50 50 20], hover time is 86400s, simulation results are as follows. Figures 4 to 7 These are the relative displacement error curve, relative velocity error curve, hovering position curve, and control force curve, respectively. The relative displacement error curve shows that the control performance meets the accuracy requirements for hovering.

[0100] As can be seen from the embodiments, the hovering control method for servicing spacecraft provided by the present invention is a finite-time control strategy that can be implemented in engineering, which is proposed for situations where the flight orbit of the current servicing spacecraft is a non-Kepler orbit, and hovering cannot generally be achieved by orbital parameter design alone. It can enable the servicing spacecraft to hover over a designated target star within a finite time and has great practical value.

[0101] In this document, the terms “comprising,” “including,” or any other variations thereof are intended to cover non-exclusive inclusion, such that a step or method that comprises a list of elements includes not only those elements but also other elements not expressly listed or inherent to such a step or method.

[0102] The above description, in conjunction with specific preferred embodiments, provides a further detailed explanation of the present invention. It should not be construed that the specific implementation of the present invention is limited to these descriptions. For those skilled in the art, various simple deductions or substitutions can be made without departing from the concept of the present invention, and all such modifications and substitutions should be considered within the scope of protection of the present invention.

Claims

1. A hovering control method for a servicing spacecraft, characterized in that, Includes the following steps: The specific steps for establishing the relative motion equations of the spacecraft include: establishing an orbital relative motion model; establishing dynamic models of the target satellite and the service spacecraft based on the orbital relative motion model; obtaining the orbital motion equations of the service spacecraft relative to the target satellite by establishing the relative position vector between the service spacecraft and the target satellite; and obtaining the final relative motion equations of the spacecraft based on the orbital motion equations by establishing the position error vector of the service spacecraft. A closed-loop controller is designed based on the relative motion equation of the spacecraft. The closed-loop controller applies continuous control force to the service spacecraft to achieve hovering of the service spacecraft relative to the target star. The target star dynamics model is as follows: (1) The dynamic model of the service spacecraft is as follows: (2) in, The gravitational constant of Earth, This represents the distance from the Earth's center to the target star. , This indicates the external perturbation force experienced by the target star. Indicates the mass of the target star. Indicates the distance from the Earth's center to the service spacecraft. , This indicates the external perturbation force experienced by the service spacecraft. Indicates the quality of the service spacecraft. For active control forces acting on servicing spacecraft, among which express The second derivative, express The second derivative; The orbital motion equations of the service spacecraft relative to the target star are obtained by establishing the relative position vector between the service spacecraft and the target star, specifically including: Let the relative position vector between the service spacecraft and the target star be... Then, from the target star dynamics model formula and the service spacecraft dynamics model formula, we obtain... (3) in In the target star's orbital coordinate system The coordinates below are represented as , exist The coordinates below are represented as ,but exist The coordinate system is represented as follows: And the distance from the Earth's center ; in and These represent the external disturbance torques experienced by the service spacecraft and the target satellite, respectively. Indicates the quality of the service spacecraft. This refers to the control force applied to the servicing spacecraft; make and exist The coordinate representations in the system are as follows: and According to the relative differentiation formula, both sides of equation (3) are projected onto Tie down, get (4) The target star's orbital angular velocity is angular acceleration is , The true perimeter angle of the target star; in Expanding equation (4), we obtain the orbital motion equation of the service spacecraft relative to the target star as follows: (5) in , , , ,in The average angular velocity of the target star, and These are the semi-major axis and eccentricity of the target star's orbit, respectively. Represents a third-order identity matrix; By establishing the service spacecraft position error vector, the final spacecraft relative motion equation is obtained based on the orbital motion equation, specifically including: Let the desired position and desired velocity of the service spacecraft be respectively... , Let the error vector of the service spacecraft be... Then, rewriting equation (5) yields the final equation of relative motion for the spacecraft: (6) in , This represents the position coordinates of the desired service spacecraft in the target star's orbital coordinate system. This represents the velocity of the desired servicing spacecraft in the target star's orbital coordinate system. This indicates the current position coordinates of the servicing spacecraft in the target star's orbital coordinate system; A closed-loop controller is designed based on the spacecraft's relative motion equations. The closed-loop controller is as follows: (7) (8) in It is a constant; Assumption It is a continuously differentiable positive definite function that satisfies , (9) in The system will then complete the task within a limited time. Converging to equilibrium point (10) A fast nonsingular sliding surface is presented based on the MSTSM method: (11) (12) in , , ,parameter for , , It is a positive number.

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