CN112597587B - Swing suppression method for recovery of failure satellite tether - Google Patents

Swing suppression method for recovery of failure satellite tether Download PDF

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CN112597587B
CN112597587B CN202011541247.6A CN202011541247A CN112597587B CN 112597587 B CN112597587 B CN 112597587B CN 202011541247 A CN202011541247 A CN 202011541247A CN 112597587 B CN112597587 B CN 112597587B
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rope
tether
tug
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CN112597587A (en
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祁瑞
姚傅祯
汤亮
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Beijing Institute of Technology BIT
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    • G06—COMPUTING; CALCULATING OR COUNTING
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    • G06F30/00—Computer-aided design [CAD]
    • G06F30/10—Geometric CAD
    • G06F30/15—Vehicle, aircraft or watercraft design
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B64—AIRCRAFT; AVIATION; COSMONAUTICS
    • B64G—COSMONAUTICS; VEHICLES OR EQUIPMENT THEREFOR
    • B64G1/00—Cosmonautic vehicles
    • B64G1/22—Parts of, or equipment specially adapted for fitting in or to, cosmonautic vehicles
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B64—AIRCRAFT; AVIATION; COSMONAUTICS
    • B64G—COSMONAUTICS; VEHICLES OR EQUIPMENT THEREFOR
    • B64G4/00—Tools specially adapted for use in space
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/10—Geometric CAD
    • G06F30/17—Mechanical parametric or variational design
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
    • G06F2119/14—Force analysis or force optimisation, e.g. static or dynamic forces

Abstract

The invention aims to solve the problem that a tether recovery excitation system vibrates after a failure satellite is captured, and provides a swing suppression method for tether recovery of the failure satellite. After being captured by the rope net, the failure satellite, the tug and the rope form a rope system towing system. The invention establishes a fine model of a rope system towing system in a three-dimensional space, a rope system is formed by a series of beads formed by connecting a spring and a damper in series, and the change of the rope system in the rope receiving process is simulated by reducing the number of the beads and changing the parameters of a tail end rope section. Aiming at the flexible spacecraft system, a feedback fluctuation control method is provided, and the swing of the system is effectively inhibited by absorbing the waves returned to the tugboat. The feedback fluctuation control can be used for towing the failed satellite while the tether is recovered, so that attitude and orbit integrated control is realized, and the system is rapidly stabilized after the tether is recovered, so that a clearing task is completed.

Description

Swing suppression method for recovery of failure satellite tether
Technical Field
The invention relates to a rope system dragging stability control method, in particular to a swing restraining method for rope system dragging and rope receiving of a failure spacecraft, which is suitable for a space debris clearing process and belongs to the technical field of aerospace.
Background
Since the first artificial earth satellite rose off in 1957, until 2016, people carried out 5000 more spacecraft launching activities, and sent 6700 more spacecrafts into earth orbit, only nearly 1400 spacecrafts in all launched spacecrafts were in effective service, while other spacecrafts became space garbage due to loss of functions. More than 260 in-orbit spacecraft or rocket disintegration/explosion/impact (fragmentation) events, producing a large amount of space debris, confirming the kesler phenomenon. With the rapid development of ultra-large scale low-orbit constellations by companies such as SpaceX and oneweb, near-earth space becomes increasingly congested and dangerous. The space debris can not only interfere with astronomical observation activities of personnel on the ground, but also have high speed (more than or equal to 7.9km/s), so that the extremely small space debris can also have larger kinetic energy, great damage is caused during collision, subsequent launching and orbit entering tasks are seriously interfered, and meanwhile, the safety of the in-orbit spacecraft is threatened. It is proven by numerical simulations that at least five large pieces of space must be actively removed each year in order to achieve a safe and stable near-earth orbit environment.
The rope system dragging system is one of the most promising active clearing technologies at present, and has the advantages of good target adaptability, high safety and the like. Tethered tow systems are typical two-tethered satellite systems, but in the classic dumbbell model, the effects of debris attitude and tether flexibility are often neglected. A bead chain model was therefore developed, simulating the transmission of force waves in the tether using a series of beads connected in series by damping springs. Since the tether system does not allow for fine manipulation of the target of the debris, the distance between the tug and the target should be gradually shortened by withdrawing the tether after capture until the mechanical arms on the tug complete a secure capture of the debris. However, since the rope-retracting process of the rope-tying system is inherently unstable, the swinging of the tied rope can be excited, further causing the swinging of the target and the tug, and easily causing a safety hazard. For example, the mechanical arm on the tug is damaged by collision with a swinging tether or target, producing more small debris, etc.
Disclosure of Invention
The invention aims to solve the problem of system oscillation and even instability caused by a rope collecting process of a rope system towing system, and provides a swing suppression method for recovering a failed satellite rope system. The method utilizes a rope system towing system, considers the fragment attitude and the characteristics of a flexible rope, establishes a bead chain model in a three-dimensional space, adopts a variable number of rope nodes to simulate the change of the length and the quality of a tied rope in the rope retracting process, designs a closed-loop fluctuation control method aiming at the system, realizes towing of the space fragments only through a tugboat propeller, inhibits the vibration caused by the recovery of the tied rope, and effectively and stably tows the space fragments to a preset track.
The purpose of the invention is realized by the following technical scheme:
the invention discloses a swing restraining method for recovering a failure satellite tether, which is characterized in that after a flying claw or a cable net on a tugboat captures fragments, in the process of recovering a tether, a three-dimensional tether towing system physical model formed by a series of half-spring damping tether connecting bead points is established, then a dynamic equation is deduced by utilizing a Newton-Euler method, and a system structure change rule in the tether recovery process is given. And by a closed-loop fluctuation control method, tether shimmy suppression and debris attitude control are realized by using a tug propeller while dragging and derailing. The method has the characteristics of strong operability, low cost and high efficiency, and is suitable for a single-rope dragging system.
The invention discloses a swing restraining method for recovering a failure satellite tether, which comprises the following steps:
the method comprises the following steps: establishing a dynamic accurate model of the rope system towing system in a recovery stage by a Newton-Euler method;
the tethered towing system consists of a tug, tethers and space debris. The tug is considered as a particle and the debris is considered as a rigid body. The tether adopts a series of bead chain models consisting of series-connected bead points of damping springs. Node B at one end of tether1Node B connected to another end of the fragmentNConnected to a tugboat, said node BNAnd the center of mass O of the tugtAnd (4) overlapping.
A variable number of rope nodes are used to simulate the change of the tied rope in the rope winding process. And (3) along with the rotation of the winch, the original length of the last section of the tether and the quality of the knot point are reduced, the knot point is removed when a certain threshold value is reached, and the two sections of the tether are combined to form a new tail end tether. In the actual rope reeling process, the end of the rope close to the winch is firstly under tension.
The initial length of the tether is L0Each rope segment has an original length of lcThe contraction speed of the tied rope is a, the number of the current rope nodes is N, and the original length of each rope section at the current moment
Figure BDA0002854931730000021
Given threshold value lrIf l is0,N-1<lrThen remove the rope node BN-1Updating the number of knots
N*＝N-1 (2)
Merging the last two segments of tether
Figure BDA0002854931730000023
The mass of the recovered tether is added to the tug, and the total mass of the system is unchanged throughout the process. Rope knot point B for connecting tugboat and fragments1、BNThe mass of each bead point is calculated by mass concentration method according to the linear density of the tether line without counting the mass
Figure BDA0002854931730000022
The reference coordinate systems are all right-handed systems and are defined as follows: earth inertial coordinate system fe(Oexeyeze)，xeThe axis always points to the spring equinox, xzThe axis points north along the earth's rotation axis; orbital coordinate system fo(Otxoyozo) Adopting a local plumb local horizontal coordinate system with an origin at the center of mass O of the tugtA, xoAxis opposite to direction of motion, zoThe shaft extends radially outward along the track; system of fragments fd(Odxdydzd) Coincident with the principal axis of inertia of the debris.
At the earth's inertial coordinatesIs fePosition vector R of lower definition tugoAnd velocity vector Vo. Orbital coordinate system foThe unit direction vector of each axis is represented as ko＝Ro/Ro，jo＝Ro×Vo/|Ro×Vo|，io＝jo×ko。RoIs the size of the track radius. Thus from the orbital coordinate system foTo the earth's inertial frame feIs a conversion matrix of
Figure BDA0002854931730000031
Using quaternion Q ═ xi0+ξ1i+ξ2j+ξ3k, the attitude motion of the tug. Obtaining a secondary orbital coordinate system foTo the system of fragments fdOf the conversion matrix
Figure BDA0002854931730000032
Wherein, I3Is a 3 × 3 identity matrix; xi0Is the real part of the quaternion, ξiIs the imaginary part, ξ, of a quaternioni＝[ξ1,ξ2,ξ3]T；
Figure BDA0002854931730000033
A cross-product matrix representing the vector is shown,
Figure BDA0002854931730000034
from the system of fragments fdTo the earth's inertial frame feIs a conversion matrix of
Figure BDA0002854931730000035
Expressing orbital motion by the number of equatorial orbitsThe number of the equatorial orbits is determined by the radius
Figure BDA0002854931730000036
Intermediate variables
Figure BDA0002854931730000037
And true longitude
Figure BDA0002854931730000038
Forming; the number of equatorial orbits is defined by adopting a classical orbit element, and the expression is as follows:
Figure BDA0002854931730000039
the classical rail element is composed of a semi-major axis
Figure BDA00028549317300000310
Eccentricity ratio
Figure BDA00028549317300000311
Inclination angle
Figure BDA00028549317300000312
Ascending crossing point of the right ascension
Figure BDA00028549317300000313
Argument of near place
Figure BDA00028549317300000314
Angle of true approach point
Figure BDA00028549317300000315
Forming; substituting the formula (5) into the orbit perturbation equation of the classical orbit element to obtain:
Figure BDA0002854931730000041
where μ is the gravitational constant, the intermediate variable
Figure BDA0002854931730000042
And
Figure BDA0002854931730000043
is defined as
Figure BDA0002854931730000044
ax，ayAnd azIs a disturbance acceleration component derived from the tether tension and tug thrust, expressed in an orbital coordinate system foThe following steps. Earth inertial coordinate system feR ofo、VoAnd an orbital coordinate system foAngular velocity of lower omegaoAngular acceleration epsilonoExpressed as:
Figure BDA0002854931730000045
Figure BDA0002854931730000046
Figure BDA0002854931730000047
Figure BDA0002854931730000048
to express the relative motion of the tethered towing system, the following generalized coordinates are chosen:
Figure BDA0002854931730000049
wherein the content of the first and second substances,
Figure BDA00028549317300000410
the rotation angle of the system of the space debris relative to the orbital coordinate system is fdArray of components of rdAnd r2,…,rN-1Respectively as the centroid O of the chipdKnot point B of the rope2,…,BN-1To the origin O of the orbital coordinate systemtIs at foAn array of lower components.
The generalized rate is then:
Figure BDA00028549317300000411
the relative motion is obtained by the difference of the motion of two objects in the same reference system, so it is necessary to find the track coordinate system f of the external force applied to the tugoThe component array of (A) is Ft＝Fg,t+Fp+FT,t. The gravity of the tugboat is
Figure BDA0002854931730000051
Wherein m istIs the tug mass.
The thrust of the engine is expressed as
Fp＝[Px Py Pz]T (18)
Wherein, Px，Py，PzRespectively, the components of the thrust force in three axes of the orbital coordinate system.
Each tether segment has a nominal length of l0,n. The nominal length l of the rope section connected with the tugboat under the action of the winch in the rope receiving process0,N-1Changes occur over time. The tension of the rope section to the tug is expressed as
Figure BDA0002854931730000052
Wherein the stiffness coefficient k of the tethern＝EA/l0,nCoefficient of damping
Figure BDA0002854931730000053
E is the Young's modulus of the tether, A is the tether cross sectionProduct, rho is the linear density of the tether, xi is the damping ratio of the tether structure, and the position vector of the N-1 th tether segment is in the earth inertia coordinate system feThe component array of (A) is
lN-1＝rN-1 (20)
A first derivative of the component array is
Figure BDA0002854931730000054
From which the relative equation of motion of the centroid of the fragments is derived
Figure BDA0002854931730000055
Wherein m isdIs the fragment mass. The gravity borne by the fragments is in a track coordinate system foThe following expression is. The C-W equation of the relative motion of two objects in space shows that the fragment is in an orbital coordinate system foIs also subjected to an inertial force D generated by the gravity of the earthd
Figure BDA0002854931730000056
Wherein R isdIs the position vector of the debris in the inertial frame f of the eartheAn array of components in (a). The tension of the tether borne by the debris is in the orbital coordinate system foThe expression below is
Figure BDA0002854931730000061
Wherein, the position vector of the 1 st rope segment is in the earth inertial coordinate system feThe component array of (A) is
l1＝r2-(rd+Ao,dρ) (25)
A first derivative of the component array is
Figure BDA0002854931730000062
Fragment in orbit coordinate system foIs also subjected to an inertial force D generated by the gravity of the earthd
Figure BDA0002854931730000063
The equation of motion of the rotation angle of the fragments is expressed as
Figure BDA0002854931730000064
Wherein, IdIs the inertia tensor, M, of the fragment in the system of fragmentsgAnd MTIn the system f of the fragments, the moments generated by the gravity gradient moment and the tether tension on the mass center of the fragmentsdComponent array of
Figure BDA0002854931730000065
Figure BDA0002854931730000066
Where ρ isdIs the position vector of the tether to fragment attachment point under the tether in the fragment.
The equation of relative motion of each rope node is
Figure BDA0002854931730000067
For any node B on the tethern(N-2, …, N-1) under its own weight in the orbital coordinate system foThe expression below is
Figure BDA0002854931730000068
The tension of the tied rope is in the track coordinate system foThe following expression is
FT,n＝Fn-1.n+Fn,n+1 (33)
Subject to inertial force in the orbital coordinate system foThe expression below is
Figure BDA0002854931730000069
Node BnThe tension of the front and the rear two sections of the tying ropes is respectively
Figure BDA0002854931730000071
Figure BDA0002854931730000072
Wherein node BnPosition vectors of front and rear rope sections in earth inertial coordinate system feThe component array of (A) is
ln-1,n＝Rn-Rn-1,ln,n+1＝Rn+1-Rn (37)
A first derivative of the component array is
Figure BDA0002854931730000073
Step two: designing a feedback fluctuation control law;
tethered towing systems are typical flexible systems. The general control does not consider the transmission of wave motion in the flexible component, and the vibration of the flexible component is inevitably excited while the control is performed. The wave control method regards the movement of the flexible system as superposition of incident waves and return waves with opposite directions, and restrains the vibration of the flexible system by absorbing the return waves. By constructing a universal, efficient, adaptable controller, the load at the free boundary can be repositioned quickly and with little vibration.
The vibration of the rope system dragging system is vertical to the transmission direction of the waves, and the rope system dragging system can be visually represented. The y-axis is plumb-up from the tug centroid and the x-axis is horizontal from the tug centroid pointing to debris. The density and the tension of the rope are constant, and the motion of the rope is described by a free vibration equation of a one-dimensional string
Figure BDA0002854931730000074
Wherein T is the tension of the tether and rho is the linear density of the tether. According to the Dalabel travelling wave decomposition, incident waves and return waves can be expressed as
Figure BDA0002854931730000075
And
Figure BDA0002854931730000076
wherein
Figure BDA0002854931730000077
Is the speed of wave propagation in the rope. Is obtained by the formula (39)
Figure BDA0002854931730000078
Figure BDA0002854931730000079
In the formula, vcIs the transverse velocity of the tug;
Figure BDA00028549317300000710
is the wave impedance of the tether,
Figure BDA00028549317300000711
representing the lateral component of the tension experienced by the tug.
The aim of the control is to smoothly change the speed of the debris to the reference speed vf. The running speed of the tugboat is always vl＝v f2, ideal speed of tug
Figure BDA0002854931730000081
The difference between the desired speed and the actual speed is converted by means of a damper into a control force acting on the tug at that moment
Figure BDA0002854931730000082
Wherein the content of the first and second substances,
Figure BDA0002854931730000083
is the damping coefficient, which is a positive number.
Horizontal thrust PxProviding an acceleration along the direction of motion of the system such that the tether remains taut; tangential thrust PyAlong yoA shaft to dampen vibration of the system out-of-plane angle; transverse thrust PzAlong zoThe shaft is used for inhibiting the vibration of the inner angle of the system surface. Obtaining a control thrust formula
Figure BDA0002854931730000084
Figure BDA0002854931730000085
Wherein the content of the first and second substances,
Figure BDA0002854931730000086
and
Figure BDA0002854931730000087
is respectively yoAxis and zoThe damping coefficient of the damper corresponding to the shaft; v. ofyAnd vzThe real-time speed of the tug under the inertial system is yoAxis and zoProjection on axis, vy＝Vo,z，
Figure BDA0002854931730000088
Vo,zIs VoAt zeThe projection on the axis is that of the lens,
Figure BDA0002854931730000089
is that
Figure BDA00028549317300000810
At zoProjection on an axis; t isyAnd TzIs the real-time tension F of the tether to the tugT,tAt yoAxis and zoProjection on the axis.
Horizontal thrust PxThe system attitude can be controlled, and simultaneously the rope system dragging system track can be maneuvered, and the tangential thrust P is combinedyAnd a lateral thrust PzThe rope dragging vibration suppression and derailment of the space debris in the rope recovery process can be realized.
Has the advantages that:
1. compared with a common dumbbell model of a tether towing system, the bead chain model considers tension delay and uneven tension distribution caused by tether flexibility, considers the space fragment posture into the model, and can predict the motion of the tether towing system more accurately.
2. According to the swing suppression method for recovering the tether of the failed satellite, disclosed by the invention, the feedback fluctuation control is adopted, so that the fragment attitude and tether swing vibration can be controlled while the orbit transfer is realized, and the risk of tether winding in the dragging process is reduced.
3. The invention discloses a swing suppression method for recovering a tether of a failed satellite, which can realize feedback fluctuation control only by a tug propeller, and eliminates the instability of a tether tension controller. The device has the advantages of high efficiency, low cost, simple structure and strong reliability.
Drawings
FIG. 1 is a schematic view of a tethered towing system according to the present invention;
FIG. 2 is a step three wave transfer model of the present invention;
FIG. 3 is a block diagram of the step three closed loop wave control of the present invention;
FIG. 4 is a graph of the relative position change of the system in an example of the present invention, where FIG. 4a) is the time history of the distance between the tug and the centroid of the debris, FIG. 4b) is the time history of the angle α inside the system plane, and FIG. 4c) is the time history of the angle β outside the system plane;
FIG. 5 is a time history of the attitude of the fragment according to an embodiment of the invention, FIG. 5a) being the roll velocity of the fragment
Figure BDA0002854931730000091
Fig. 5b) is the time history of the pitch velocity θ of the debris, fig. 5c) is the time history of the yaw velocity ψ of the debris, fig. 5d) is the roll angular velocity of the debris
Figure BDA0002854931730000092
Time history of (5 e) is the chip pitch angle velocity
Figure BDA0002854931730000093
Time history of (5 f) is the chip yaw rate
Figure BDA0002854931730000094
The time history of (d);
FIG. 6 is a tether tension time history of a connected fragment in an example of the invention;
fig. 7 is a real-time track height curve for a rope towing system in an example of the invention.
Detailed Description
For better illustrating the objects and advantages of the present invention, the following description is provided in conjunction with the accompanying drawings and examples.
Example 1:
assuming that the tether towing system is located on a geosynchronous circular orbit with an orbit radius of 42164km at the initial moment, the number of rope nodes of the ball chain model is 21. The pitch and yaw directions of the debris at capture each have an initial angular velocity of 5/s. The tether retrieval task requires shrinking the original length 100m to 20 m. The system parameters are shown in the table below.
Table 1 initial parameters of a tethered towing system
Figure BDA0002854931730000095
The method comprises the following steps: launching the trailer spacecraft into orbit to capture space debris;
step two: establishing a three-dimensional attitude and orbit coupling dynamics accurate model of the rope system towing system by a Newton-Euler method;
step three: making a rope winding strategy;
a variable number of rope nodes are used to simulate the change of the tied rope in the rope winding process. And (3) along with the rotation of the winch, the original length of the last section of the tether and the quality of the knot point are reduced, the knot point is removed when a certain threshold value is reached, and the two sections of the tether are combined to form a new tail end tether. In the actual rope reeling process, the end of the rope close to the winch is firstly under tension. The nominal length of the tied rope is reduced when the rope is reeled, but the actual length of the tied rope is also reduced, but the actual length cannot be suddenly changed in the process of simulation iteration, so that the theoretical deformation of the tied rope at the tail end is larger than the actual deformation, the tension of the tied rope is abnormal, and the system distortion can be caused if the rope reeling speed is too high. It is therefore necessary to redefine the stiffness coefficient of the end rope portions
Figure BDA0002854931730000101
Wherein k is the theoretical stiffness coefficient of the tail end rope section, and a is the contraction speed of the tether. The initial length of the tether is L0The original length of each rope section is the same as lc. The number of the current rope nodes is N, the original length of each rope section at the moment
Figure BDA0002854931730000102
Given threshold value lrIf l isN-1<lrThen remove the ropeNode BN-1Updating the number of knots
N*＝N-1 (3)
Merging the last two segments of tether
Figure BDA0002854931730000103
In the process of contracting the tether from 100m to 20m, the number of knot points is gradually changed from 21 to 5. Since the recovery speed of the tether is set to 0.1m/s, the hoist stops when the original length of the tether becomes 20m, which may cause the system to be unstable. At t-40, 90,140,190,240,290,340,390,440,490,540,590,640,690,740,790s, the tether tie point closest to the tug is deleted.
The mass of the recovered tether is added to the tug, and the total mass of the system is unchanged throughout the process. Rope knot point B for connecting tugboat and fragments1、BNThe mass is not counted, and the mass of other bead points is obtained by a mass concentration method according to the linear density of the tether
Figure BDA0002854931730000104
Step four: designing a closed-loop fluctuation control law;
the vibration of the rope system dragging system is vertical to the transmission direction of the waves, and the rope system dragging system can be visually represented. The y-axis is plumb-up from the tug centroid and the x-axis is horizontal from the tug centroid pointing to debris. The density and the tension of the rope are constant, and the motion of the rope is described by a free vibration equation of a one-dimensional string
Figure BDA0002854931730000111
Wherein T is the tension of the tether and rho is the linear density of the tether. According to the Dalabel travelling wave decomposition, incident waves and return waves can be expressed as
Figure BDA0002854931730000112
And
Figure BDA0002854931730000113
wherein
Figure BDA0002854931730000114
Is the speed of wave propagation in the rope. In practice, the wave speed can be regarded as a constant value, with the real-time tension being replaced by the mean tension,
Figure BDA0002854931730000115
is obtained by the formula (6)
Figure BDA0002854931730000116
Figure BDA0002854931730000117
The goal of the control is to suppress the roping trailed system hunting. Assuming a virtual tug in front of the tug, and passing a damping coefficient cnIs connected with the damper. In order to stabilize the system, making the incident wave constant,
Figure BDA0002854931730000118
the speed of the virtual tug can be suddenly changed and kept at the ideal speed all the time
Figure BDA0002854931730000119
Wherein, the first and the second end of the pipe are connected with each other,
Figure BDA00028549317300001110
is the tether impedance, determined by the tether properties and tension, and can be expressed as
Figure BDA00028549317300001111
The difference between the ideal speed and the actual speed causes the damper to generate a damping force, i.e. a lateral control force, tangential and radial, acting on the tug at the present momentThe formula of the control thrust is
Figure BDA00028549317300001112
Figure BDA00028549317300001113
Wherein the damping coefficient is set to
Figure BDA00028549317300001114
And
Figure BDA00028549317300001115
respectively, tension F experienced by the tugT,tAt yoAxis and zoProjection on an axis; v. ofyAnd vzThe real-time speed of the tug under the inertial system is yoAxis and zoProjection on axis, vy＝Vo,z，
Figure BDA00028549317300001116
Vo,zIs a VoAt zeThe projection on the axis is that of the lens,
Figure BDA00028549317300001117
is that
Figure BDA00028549317300001118
At zoProjection on the axis.
The horizontal thrust can maintain the system posture and keep the tether tensioning while changing the system track, so the larger the value of the horizontal thrust is, the more beneficial the system stability is, the setting P isx50N. To prevent the thrust from exceeding the propeller constraint, let PyAnd PzThe maximum value is 50N.
Step five: igniting and propelling, starting the rope-tied winch and carrying out numerical simulation;
and (4) performing simulation according to the parameters, and simultaneously integrating the motion differential equation and the orbit perturbation equation to obtain the images of fig. 4, fig. 5, fig. 6 and fig. 7. Before 800s, the fragment amplitude is limited within 1 degree as shown in figure 5, which shows that the fluctuation control can effectively restrain the vibration of the rope system dragging system in time during the rope winding process. At 800s the tether retrieval stopped and the tether towing system was excited to vibrate, the system in-plane and out-of-plane angular amplitudes were greater than at the initial moment, the debris had been despuned and the amplitudes of yaw and pitch angles were only slightly increased compared to those before 800 s. The surface corresponds to the vibration generated by the tether stopping contraction, the feedback fluctuation control has extremely strong robustness, can quickly respond, and the posture stabilization of the system is completed within 800 s. It can be known from fig. 4, 5 and 6 that the system always generates vibration during the rope winding process, and the feedback fluctuation control cannot completely absorb vibration energy, and can only suppress the vibration within a range, thereby meeting the requirements of most space debris cleaning tasks. After the tether towing system finishes tether recovery, the fluctuation control can continuously absorb vibration energy until the vibration is completely eliminated. As shown in fig. 7, while suppressing vibration, the horizontal thrust also causes the system to become orbital, increasing the efficiency of the space debris removal task.
The above detailed description is intended to illustrate the objects, aspects and advantages of the present invention, and it should be understood that the above detailed description is only exemplary of the present invention and is not intended to limit the scope of the present invention, and any modifications, equivalents, improvements and the like made within the spirit and principle of the present invention should be included in the scope of the present invention.

Claims (1)

1. A swing restraining method for recovering a failure satellite tether is characterized by comprising the following steps: the method comprises the following steps:
the method comprises the following steps: establishing a dynamic accurate model of the rope system towing system in a recovery stage by a Newton-Euler method;
the rope system towing system consists of a tugboat, a tether and space debris, wherein the tugboat is regarded as mass points, the debris is regarded as rigid bodies, the tether adopts a ball chain model consisting of a series of ball points connected in series by damping springs, and a node B at one end of the tether1Node B connected to another end of the fragmentNConnected to a tugboat, said node BNAnd the center of mass O of the tugtOverlapping;
the method comprises the following steps that the change of a tied rope in the rope winding process is simulated by adopting the rope nodes with variable quantity, along with the rotation of a winch, the original length of the last section of the tied rope and the quality of the rope nodes are reduced, the rope nodes are removed when a certain threshold value is reached, two sections of tied ropes are combined to form a new tail end tied rope, and in the actual rope winding process, one end of the tied rope close to the winch is firstly under the action of tension;
the initial length of the tether is L0Each rope segment has an original length of lcThe contraction speed of the tied rope is a, the number of the current rope nodes is N, and the original length of each rope section at the current moment
Figure FDA0003612380730000011
Given threshold value lrIf l is0,N-1＜lrThen remove the rope node BN-1Updating the number of knots
N*＝N-1 (2)
Merging the last two segments of tether
Figure FDA0003612380730000012
The mass of the recovered tether is added to the tug, the total mass of the system is unchanged in the whole process, and a tether junction B connecting the tug and the fragments1、BNThe mass of each bead point is calculated by mass concentration method according to the linear density of the tether line without counting the mass
Figure FDA0003612380730000013
The reference coordinate systems are all right-handed systems and are defined as follows: earth inertial coordinate system fe(Oexeyeze)，xeThe axis always points to the spring equinox, xzAxis along the earthThe rotating shaft points to the north; orbital coordinate system fo(Otxoyozo) Adopting a local plumb local horizontal coordinate system with an origin at the center of mass O of the tugtA, xoAxis opposite to direction of movement, zoThe shaft extends radially outward along the track; system of fragments fd(Odxdydzd) Coincident with the principal axis of inertia of the debris;
in the earth's inertial frame fePosition vector R of lower definition tugoAnd velocity vector VoOrbital coordinate system foThe unit direction vector of each axis is represented as ko＝Ro/Ro，jo＝Ro×Vo/|Ro×Vo|，io＝jo×ko，RoIs the size of the track radius and is therefore derived from the track coordinate system foTo the earth's inertial frame feIs a conversion matrix of
Figure FDA0003612380730000021
Using quaternion Q ═ xi0+ξ1i+ξ2j+ξ3k, representing the attitude motion of the tug, resulting in a slave orbital coordinate system foTo the system of fragments fdIs converted into a matrix
Figure FDA0003612380730000022
Wherein, I3Is a 3 × 3 identity matrix; xi0Is the real part of the quaternion, ξiIs the imaginary part, ξ, of a quaternioni＝[ξ1,ξ2,ξ3]T；
Figure FDA0003612380730000023
A cross-product matrix representing the vector is represented,
Figure FDA0003612380730000024
from the system of fragments fdTo the earth's inertial frame feIs a conversion matrix of
Figure FDA0003612380730000025
Expressing orbital motion by using the number of equatorial orbits which is formed by a half-diameter
Figure FDA0003612380730000026
Intermediate variables
Figure FDA0003612380730000027
And true longitude
Figure FDA0003612380730000028
Forming; the number of the equatorial orbits is defined by adopting the classical orbit elements, and the expression is as follows:
Figure FDA0003612380730000029
the classical rail element is composed of a semi-major axis
Figure FDA00036123807300000210
Eccentricity ratio
Figure FDA00036123807300000211
Inclination angle
Figure FDA00036123807300000212
Ascending crossing point of the right ascension
Figure FDA00036123807300000213
Argument of near place
Figure FDA00036123807300000214
Angle of true approach point
Figure FDA00036123807300000215
Forming; substituting the formula (5) into the orbit perturbation equation of the classical orbit element to obtain:
Figure FDA00036123807300000216
where μ is the gravitational constant, the intermediate variable
Figure FDA00036123807300000217
And
Figure FDA00036123807300000218
is defined as
Figure FDA00036123807300000219
ax，ayAnd azIs a disturbance acceleration component derived from tether tension and tug thrust, expressed in an orbital coordinate system foLower, earth inertial coordinate system feR ofo、VoAnd an orbital coordinate system foLower angular velocity ωoAngular acceleration epsilonoExpressed as:
Figure FDA0003612380730000031
Figure FDA0003612380730000032
Figure FDA0003612380730000033
Figure FDA0003612380730000034
to express the relative motion of the tethered towing system, the following generalized coordinates are chosen:
Figure FDA0003612380730000035
wherein, the first and the second end of the pipe are connected with each other,
Figure FDA0003612380730000036
the rotation angle of the system of the space debris relative to the orbital coordinate system is fdArray of components of rdAnd r2,…,rN-1Respectively as the centroid O of the chipdKnot point B of the rope2,…,BN-1To the origin O of the orbital coordinate systemtIs at foA component array of down;
the generalized rate is then:
Figure FDA0003612380730000037
the relative motion is obtained by the difference of the motion of two objects in the same reference system, so it is necessary to find the track coordinate system f of the external force applied to the tugoThe component array of (A) is Ft＝Fg,t+Fp+FT,tThe gravity of the tugboat is
Figure FDA0003612380730000038
Wherein m istIs the tug mass;
the thrust of the engine is expressed as
Fp＝[Px Py Pz]T (18)
Wherein, Px，Py，PzThe components of the thrust under three axes of the orbit coordinate system are respectively;
each tether segment has a nominal length of l0,nAnd the nominal length l of the rope section connected with the tugboat under the action of the winch in the rope collecting process0,N-1The tension of the rope portion to the tug is expressed as
Figure FDA0003612380730000041
Wherein the stiffness coefficient k of the tethern＝EA/l0,nCoefficient of damping
Figure FDA0003612380730000042
E is the Young modulus of the tether, A is the cross section area of the tether, rho is the linear density of the tether, xi is the damping ratio of the tether structure, and the position vector of the N-1 th tether section is in the earth inertia coordinate system feThe component array of (A) is
lN-1＝rN-1 (20)
A first derivative of the component array is
Figure FDA0003612380730000043
From which the relative equation of motion of the centroid of the fragments is derived
Figure FDA0003612380730000044
Wherein m isdIs the mass of the fragment, and the gravity borne by the fragment in the orbital coordinate system foThe expression below is
Figure FDA0003612380730000045
Wherein R isdIs the inertial coordinate of the fragment position vector on the earthIs feMedium component array, the tension of the tied rope on the broken piece is in the orbit coordinate system foThe expression below is
Figure FDA0003612380730000046
Wherein, the position vector of the 1 st rope segment is in the earth inertial coordinate system feThe component array of (A) is
l1＝r2-(rd+Ao,dρ) (25)
A first derivative of the component array is
Figure FDA0003612380730000047
The C-W equation of the relative motion of two objects in space shows that the fragment is in an orbital coordinate system foIs also subjected to an inertial force D generated by the gravity of the earthd
Figure FDA0003612380730000048
The equation of motion of the rotation angle of the fragments is expressed as
Figure FDA0003612380730000051
Wherein, IdIs the inertia tensor, M, of the fragment in the system of fragmentsgAnd MTIn the system f of the fragments, the moments generated by the gravity gradient moment and the tether tension on the mass center of the fragmentsdComponent array of
Figure FDA0003612380730000052
Figure FDA0003612380730000053
Wherein ρdIs the position vector of the tether and fragment attachment point under the tether in the fragment;
the equation of relative motion of each rope node is
Figure FDA0003612380730000054
For any node B on the tethernWherein N is 2, …, N-1, and receives its own gravity in the orbit coordinate system foThe expression below is
Figure FDA0003612380730000055
The tension of the tied rope is in the track coordinate system foThe expression below is
FT,n＝Fn-1.n+Fn,n+1 (33)
Subject to inertial force in the orbital coordinate system foThe expression below is
Figure FDA0003612380730000056
Node BnThe tension of the front and the rear two sections of the tying ropes is respectively
Figure FDA0003612380730000057
Figure FDA0003612380730000058
Wherein node BnPosition vectors of front and rear rope sections in earth inertial coordinate system feThe component array of (A) is
ln-1,n＝Rn-Rn-1,ln,n+1＝Rn+1-Rn (37)
A first derivative of the component array is
Figure FDA0003612380730000061
Step two: designing a feedback fluctuation control law;
the rope system towing system is a typical flexible system, the transmission of wave motion in the flexible component cannot be considered in general control, the vibration of the flexible component is inevitably excited during the control, the wave motion control method regards the motion of the flexible system as the superposition of incident wave and return wave with opposite directions, the vibration of the flexible system is inhibited by absorbing the return wave, and the load at the free boundary can be quickly and almost vibrationless repositioned by constructing a universal, efficient and adaptable controller;
the vibration of the rope system towing system is vertical to the transmission direction of the waves and can be visually represented, the y axis is vertically upward from the center of mass of the tugboat, the x axis is horizontally directed to fragments from the center of mass of the tugboat, the density and the tension of the rope are constants, and the motion of the rope is described by a free vibration equation of a one-dimensional string
Figure FDA0003612380730000062
Wherein T is the tension of the tether, and rho is the linear density of the tether; according to the Dalabel travelling wave decomposition, incident waves and return waves can be expressed as
Figure FDA0003612380730000063
And
Figure FDA0003612380730000064
wherein
Figure FDA0003612380730000065
For the propagation velocity of waves in the rope, obtained by equation (39)
Figure FDA0003612380730000066
Figure FDA0003612380730000067
In the formula, vcIs the transverse velocity of the tug;
Figure FDA0003612380730000068
is the wave impedance of the tether,
Figure FDA0003612380730000069
Figure FDA00036123807300000610
a lateral component representing the tension experienced by the tug;
the aim of the control is to smoothly change the speed of the debris to the reference speed vfThe advancing speed of the tugboat is always vl＝vf2, ideal speed of tug
Figure FDA00036123807300000611
The difference between the desired speed and the actual speed is converted by a damper into a control force acting on the tug at that moment
Figure FDA00036123807300000612
Wherein the content of the first and second substances,
Figure FDA00036123807300000613
is the damping coefficient, which is a positive number;
horizontal thrust PxProviding an acceleration along the direction of motion of the system such that the tether remains taut; tangential thrust PyAlong yoA shaft to dampen vibration of the system out-of-plane angle; transverse thrust PzAlong zoShaft for suppressing the vibration of the system face internal angle to obtain the control thrust formula
Figure FDA0003612380730000071
Figure FDA0003612380730000072
Wherein the content of the first and second substances,
Figure FDA0003612380730000073
and
Figure FDA0003612380730000074
is respectively yoAxis and zoThe damping coefficient of the damper corresponding to the shaft; v. ofyAnd vzThe real-time speed of the tug under the inertial system is yoAxis and zoProjection on axis, vy＝Vo,z，
Figure FDA0003612380730000075
Vo,zIs VoAt zeThe projection on the axis is that of the lens,
Figure FDA0003612380730000076
is that
Figure FDA0003612380730000077
At zoProjection on an axis; t isyAnd TzIs the real-time tension F of the tether to the tugT,tAt yoAxis and zoProjection on an axis;
horizontal thrust PxIn the control system of postureThe state can also make the rope system dragging system orbit generate maneuver at the same time, and the tangential thrust P is combinedyAnd a lateral thrust PzThe rope dragging vibration suppression and derailment of the space debris in the rope recovery process can be realized.
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