CN106020217A - Reel-controlled towing orbital transfer anti-winding and anti-collision method - Google Patents

Abstract

The invention discloses a reel-controlled towing orbital transfer anti-winding and anti-collision method. The method achieves towing orbital transfer anti- winding and anti-collision by establishing a combination orbital transfer dynamical model taking account of attitude at both ends and the loosening of a rope, establishing the reel control module and a winding model of the rope, designing an anti-collision/winding reel control law, and designing a platform attitude control law. Compared with a conventional model taking account of the spacecraft attitude, the method in the invention is applicable to a tense rope state or a loosened rope state. The method designs the reel control law to regulate the tension of the rope. The reel control law may control tension more directly and proactively than thrust filter technique and does not influence the application of the prior art. As a result, the control strategy undoubtedly relieves the burden of platform thrust and provides large degree of freedom for orbital design.

Description

A kind of towing utilizing spool to control becomes the antiwind collision-proof method of rail

[technical field]

The invention belongs to the spacecraft maneuver of rope system and become rail research field, be specifically related to robot of space rope system in towing The antiwind method of anticollision during objective body.

[background technology]

The track rubbish towing using robot of space rope system removes, and enjoys because of its high flexibility and high security Attract attention.

Robot of space rope system uses flexible tether to replace traditional mechanical arm to carry out space operation.But tether is had The single spring performance having, provides pulling force and non-pusher the most only, easily cause the collision of two ends spacecraft and they Winding with tether.Collision can cause more space debris, the aggravation threat to rail safety, therefore collides Harm self-evident, but the adverse effect being wound around is difficult to imagine.In fact as a class noncooperative target, Objective body to be pulled is typically unstable.It is in lax shape at the such spacecraft of towing once tether State, then can be wound around with objective body moment, makes the rope length between the spacecraft of two ends die-off.When tether is tightened again Time, owing to there is speed of wrap faster, tether tension force can be caused to increase sharply.Bigger tension force is by two ends spacecraft Being pulled towards each other, thing followed collision will occur.Visible, for ensureing being smoothed out of towing task, collision All must avoid with being wound around.Above the analysis being wound around mechanism can be drawn a conclusion, either in collision still In winding, tether tension force all plays decisive role.Therefore, the conservative control to tether tension force is that anticollision is prevented The key being wound around.

For this, domestic scholars becomes the antiwind aspect of rail anticollision in towing and proposes many new suggested, delivers Document have: " the Dynamics of of " SCIENCE CHINA Technological Sciences " tether-tugging reorbiting with net capture》.This research shows that the initial attitude of two ends spacecraft is consistent Time, tether tension force can tend towards stability during towing, be avoided that the generation of collision.Once their initial appearance State has deviation, then tension force by out of control and cause collision

Comparing the more domestic anticollision strategy adjusting initial attitude, foreign scholar is at " Acta Astronautica " On " the Input shaped large thrust maneuver with a tethered debris object " that deliver and In " Tethered towing using open-loop input-shaping and discrete thrust levels ", use Platform thrust filtering technique, can make tether tension force comply with the change of thrust passively and make corresponding adjustment. Such as when tail-off, tension force can drop to rapidly zero collision free.Additionally, be published in " Transactions On Robotics and Automation " on " Attitude stabilization of an unknown and spinning Target spacecraft using a visco-elastic tether " have employed the mode that assembly system for winding barycenter rotates Tether is made under centrifugal force to be in tensioning state, thus collision free.But, these strategies are to tether tension force Can only carry out passive regulation and all rely on external force, such as platform thrust, this can affect the design becoming rail track.

[summary of the invention]

It is an object of the invention to provide a kind of the antiwind towing of the anticollision utilizing platform spool to control and become rail Method.The method does not affect the normal applying of platform thrust, carries out extra Filtering Processing without to thrust, The biggest space can be provided to orbit Design.

For reaching above-mentioned purpose, the present invention is achieved by the following technical solutions:

A kind of towing utilizing spool to control becomes the antiwind collision-proof method of rail, comprises the following steps:

1) the assembly change rail kinetic model considering that two ends attitude and tether are lax is set up；

Lagrangian method is utilized to set up assembly orbital plane internal dynamics model:

$\begin{array}{c}{\stackrel{\·\·}{r}}_1=r_1{\stackrel{\·}{\mathrm{\α}}}_1^2-\frac{\mathrm{\μ}}{r_1^2}+\frac{1}{m_1+m_2}\{m_2\stackrel{\·\·}{s}\sin \mathrm{\β}-\frac{3{\mathrm{\μm}}_2{s}^2}{r_1^4}+\frac{9{\mathrm{\μm}}_2{s}^2{\cos }^2\mathrm{\β}}{2r_1^4}\\ +m_2\cos \mathrm{\β}\[s({\stackrel{\·\·}{\mathrm{\α}}}_1-\stackrel{\·\·}{\mathrm{\β}})+2\stackrel{\·}{s}({\stackrel{\·}{\mathrm{\α}}}_1-\stackrel{\·}{\mathrm{\β}})\]-m_{2}s\sin \mathrm{\β}{({\stackrel{\·}{\mathrm{\α}}}_1-\stackrel{\·}{\mathrm{\β}})}^2\\ -\frac{2{\mathrm{\μm}}_{2}s\sin \mathrm{\β}}{r_1^3}+Q_{r1}\}\end{array}$

$\begin{array}{c}{\stackrel{\·\·}{\mathrm{\α}}}_1=\frac{1}{m_2(r_1^2+s^2-2{\mathrm{sr}}_1\sin \mathrm{\β})+I_1+I_2+m_1{r}_1^2}\{-2m_2\stackrel{\·}{s}{r}_1\sin \mathrm{\β}(\stackrel{\·}{\mathrm{\β}}-{\stackrel{\·}{\mathrm{\α}}}_1)\\ +\[-I_1{\stackrel{\·\·}{\mathrm{\θ}}}_1-I_2{\stackrel{\·\·}{\mathrm{\θ}}}_2+I_2-m_2({\mathrm{sr}}_1\sin \mathrm{\β}-s^2)\]\stackrel{\·\·}{\mathrm{\β}}-m_2\cos \mathrm{\β}(s{\stackrel{\·\·}{r}}_1+r_1\stackrel{\·\·}{s})\\ -m_{2}s(r_1{\stackrel{\·}{\mathrm{\β}}}^2\cos \mathrm{\β}-2r_1{\stackrel{\·}{\mathrm{\α}}}_1\stackrel{\·}{\mathrm{\β}}\cos \mathrm{\β}-2{\stackrel{\·}{r}}_1{\stackrel{\·}{\mathrm{\α}}}_1\sin \mathrm{\β})+m_2{\stackrel{\·}{r}}_1\stackrel{\·}{s}\cos \mathrm{\β}\\ -2m_{2}s\stackrel{\·}{s}({\stackrel{\·}{\mathrm{\α}}}_1-\stackrel{\·}{\mathrm{\β}})-m_2{r}_1\stackrel{\·}{s}\stackrel{\·}{\mathrm{\β}}\sin \mathrm{\β}-2r_1{\stackrel{\·}{r}}_1{\stackrel{\·}{\mathrm{\α}}}_1(m_1+m_2)+Q_{\mathrm{\α}1}\}\end{array}$

$\begin{array}{c}{\stackrel{\·\·}{\mathrm{\θ}}}_1=\frac{1}{I_1}\{Q_{\mathrm{\θ}1}-I_1{\stackrel{\·\·}{\mathrm{\α}}}_1-l_{rt}^{-1}\mathrm{\λ}EA\[-x_d\cos (\mathrm{\β}+{\mathrm{\θ}}_1)+y_d\sin (\mathrm{\β}+{\mathrm{\θ}}_1)\]\\ \·\[l_{rt}-s-y_d\cos (\mathrm{\β}+{\mathrm{\θ}}_1)-x_d\sin (\mathrm{\β}+{\mathrm{\θ}}_1)+y_p{\mathrm{cos\θ}}_2+x_p{\mathrm{sin\θ}}_2\]\}\end{array}$

$\begin{array}{c}\stackrel{\·\·}{\mathrm{\β}}=\frac{1}{m_2{s}^2+I_2}\{(m_2{s}^2+I_2-m_2{r}_{1}s\sin \mathrm{\β}){\stackrel{\·\·}{\mathrm{\α}}}_1+I_2{\stackrel{\·\·}{\mathrm{\θ}}}_2+m_{2}s\cos \mathrm{\β}{\stackrel{\·\·}{r}}_1\\ +2m_{2}s\stackrel{\·}{s}({\stackrel{\·}{\mathrm{\α}}}_1-\stackrel{\·}{\mathrm{\β}})-l_{rt}^{-1}\mathrm{\λ}EA\[-x_d\cos (\mathrm{\β}+{\mathrm{\θ}}_1)+y_d\sin (\mathrm{\β}+{\mathrm{\θ}}_1)\]\\ \·\[l_{rt}-s-y_d\cos (\mathrm{\β}+{\mathrm{\θ}}_1)-x_d\sin (\mathrm{\β}+{\mathrm{\θ}}_1)+y_p{\mathrm{cos\θ}}_2+x_p{\mathrm{sin\θ}}_2\]\\ -2m_{2}s{\stackrel{\·}{\mathrm{\α}}}_1{\stackrel{\·}{r}}_1\sin \mathrm{\β}+\frac{3{\mathrm{\μm}}_2{s}^2\sin 2\mathrm{\β}}{2r_1^3}+\frac{{\mathrm{\μm}}_{2}s\cos \mathrm{\β}}{r_1^2}-m_2{\mathrm{sr}}_1{\stackrel{\·}{\mathrm{\α}}}_1^2+Q_{\mathrm{\β}}\}\end{array}$

$\begin{array}{c}\stackrel{\·\·}{s}={\stackrel{\·\·}{r}}_1\sin \mathrm{\β}+r_1{\stackrel{\·\·}{\mathrm{\α}}}_1\cos \mathrm{\β}+\frac{1}{m_2}\{m_{2}s{({\stackrel{\·}{\mathrm{\α}}}_1-\stackrel{\·}{\mathrm{\β}})}^2+\mathrm{\λ}EA(1-\frac{s}{l_{rt}})\\ +2m_2{\stackrel{\·}{\mathrm{\α}}}_1{\stackrel{\·}{r}}_1\cos \mathrm{\β}-m_2{r}_1{\stackrel{\·}{\mathrm{\α}}}_1^2\sin \mathrm{\β}+\frac{{\mathrm{\μm}}_{2}s}{2r_1^3}+\frac{{\mathrm{\μm}}_2\sin \mathrm{\β}}{r_1^2}\\ -\frac{3{\mathrm{\μm}}_{2}s\cos 2\mathrm{\β}}{2r_1^3}+l_{rt}^{-1}\mathrm{\λ}EA\[-y_d\cos (\mathrm{\β}+{\mathrm{\θ}}_1)-x_d\sin (\mathrm{\β}+{\mathrm{\θ}}_1)\\ +y_p{\mathrm{cos\θ}}_2+x_p{\mathrm{sin\θ}}_2\]+Q_s\}\end{array}$

$\begin{array}{c}{\stackrel{\·\·}{\mathrm{\θ}}}_2=\stackrel{\·\·}{\mathrm{\β}}-{\stackrel{\·\·}{\mathrm{\α}}}_1+\frac{1}{I_2}\{-l_{rt}^{-1}\mathrm{\λ}EA(x_p{\mathrm{cos\θ}}_2-y_p{\mathrm{sin\θ}}_2)\[l_{rt}-s+y_p{\mathrm{cos\θ}}_2\\ -y_d\cos (\mathrm{\β}+{\mathrm{\θ}}_1)-x_d\sin (\mathrm{\β}+{\mathrm{\θ}}_1)+x_p{\mathrm{sin\θ}}_2\]+Q_{\mathrm{\θ}2}\}\end{array}$

Wherein, q=[r₁,α₁,θ₁,β,s,θ₂]^TFor 6DOF generalized coordinates, r in assembly orbital plane₁Put down for space Platform barycenter orbit radius, α₁For platform barycenter true anomaly, θ₁For platform pitch attitude angle, β is two ends space flight Device barycenter line and local horizontal line angle (face interior angle), s is two ends spacecraft centroid lines, θ₂For objective body Pitch attitude angle, l_rtLong for the rope after deduction coiling length, m₁For platform mass, m₂For objective body quality, I₁ For platform pitch rotation inertia, I₂For objective body pitch rotation inertia；λ is tether relaxation factor, and relaxing is 0 Tensioning is 1；EA is tether rigidity；Each generalized force Q_r1、Q_α1、Q_θ1、Q_β、Q_s、Q_θ2Define with tether tension force As follows:

$\left\{\begin{array}{c}{Q}_{r1}=-F{\mathrm{sin\θ}}_1\\ Q_{\mathrm{\α}1}={\mathrm{Fr}}_1{\mathrm{cos\θ}}_1\\ Q_{\mathrm{\θ}1}={\mathrm{\τ}}_c\\ Q_{\mathrm{\β}}=0\\ Q_s=0\\ Q_{\mathrm{\θ}2}=0\end{array}\right.T=\left\{\begin{array}{cc}\frac{EA(l-l_{rt})}{l_{rt}}& l>l_{rt}\\ 0& l\≤l_{rt}\end{array}\right.$

Wherein, F is space platform thrust, τ_cFor platform stance control moment,For tether point of release in space Vector under platform body system,The vector arrested a little under complex for tether,For being referred to by point of release To the tension force vector arrested a little,For by arrest the tension force that points to point of release to；φ is tether and two barycenter company The angle of line, its with deformation after the long l of rope be defined as follows:

Wherein, (x_d,y_d) it is point of release coordinate, (x under platform body system_p,y_p) for arresting a little under complex Coordinate；

2) set up the spool Controlling model of tether and be wound around model；

Tether spool Controlling model:

The moment of momentum theorem is used to set up spool kinetic model as follows:

$I_r{\stackrel{\·\·}{\mathrm{\φ}}}_r+C_d{\stackrel{\·}{\mathrm{\φ}}}_r=Tr-T_m$

$r=\sqrt{s_2-s_1{l}_r}$

${\mathrm{\φ}}_r=-\frac{2}{S_1}\sqrt{S_2-S_1{l}_r}+\frac{2\sqrt{S_2}}{S_1}$

$S_1=\frac{r_d^2}{w_d}{S}_2=S_1{L}_r+R_1^2$

Wherein, I_rFor spool rotary inertia, φ_rFor spool corner, C_dFor spool damped coefficient, r is spool half Footpath, T_mFor reel motor control moment, l_rNot deformed rope for spool release is long, r_dFor tether diameter, w_dFor Spool width, R₁For without spool radius during tether, L_rLong for spool maximum release rope；

Tether winding model:

Assume initially that the rectangle that space platform is a × b m, objective body and intelligence fly pawl and be considered as an entirety, for the length of side It it is the square of cm；Secondly for space platform from the beginning of the summit on the downside of tether point of release, by side clockwise Number to each summit, be followed successively by 0,1,2,3；For objective body from the beginning of the summit arresting a upside, still by suitable Clockwise carries out summit numbering, is followed successively by 0,1,2,3；When two ends spacecraft and tether occur to be wound around, space flight Tether junction point on device will be moved on corresponding summit, and tether junction point is point of release or arrests a little；

Definition platform winding angle ψ=θ₁+ β-φ, and objective body winding angle η=θ₂-φ, wherein, ψ is tether and this The angle of body wobble shaft negative sense, η is the angle of tether and objective body wobble shaft forward；When they meet following bar During part, then it is assumed that be wound around and occur:

Definition tw is for being wound around coefficient, and cn is for being wound around the number of turns, l_twpFor platform coiling length, l_twdIt is wound around for objective body Length, flag is for being wound around point (summit) sequence number；Wherein cn is expressed as: cn=[tw/4], and [] is rounding operation symbol, And institute's round numbers is less than the number in operator；If point of release is respectively with arresting respective initial coordinate a little (x_d0,y_d0) and (x_p0,y_p0)；

For platform:

For objective body:

Therefore total coiling length is l_tw=l_twp+l_twd, a length of l of not deformed rope of actual deduction coiling length_rt=l_r-l_tw；

3) the spool design of control law of anticollision/winding；

First the tension force after estimating system is stable:

$\hat{T}=\frac{m_{2}F}{m_1+m_2}$

Determine tension restriction scope:

$T_{min}=\frac{1}{2}\hat{T},T_{max}=\frac{3}{2}\hat{T}$

Wherein the tension force upper limit retrains if it exceeds thrust, then set thrust as the tension force upper limit；

Calculating tension restriction equivalence spool corner:

${\mathrm{\φ}}_{rd\min }=-\frac{2}{S_1}\sqrt{S_2-S_1(\frac{l}{1+T_{\min }/EA}+l_{tw})}+\frac{2\sqrt{S_2}}{S_1}$

${\mathrm{\φ}}_{rdmax}=-\frac{2}{S_1}\sqrt{S_2-S_1(\frac{l}{1+T_{\max }/EA}+l_{tw})}+\frac{2\sqrt{S_2}}{S_1}$

Calculating spool corner tracking error:

${\mathrm{\&Omega;}}_r=\left\{\begin{array}{cc}{\mathrm{\&phi;}}_{rdmax}-{\mathrm{\&phi;}}_r& T\&GreaterEqual;T_{max}\\ {\stackrel{\&CenterDot;}{\mathrm{\&phi;}}}_r& T_{\min }<T<T_{max}\\ {\mathrm{\&phi;}}_{rd\min }-{\mathrm{\&phi;}}_r& T\&le;T_{\min }\end{array}\right.$

Wherein tension force uses and triggers control strategy, just carries out tension force control time outside only tether tension force is in constraint System, then maintains the long holding of rope constant within it is in restriction range, allows tension force freely change；

The speed sliding-mode surface of definition spool corner is:

Wherein k₁And k₂For normal number,For fast Sliding Mode Track deviation, ω_rcFor the virtual control of corner speed Amount processed is pushed away by slow sliding formwork Equivalent control law, λ₁For anti-saturation module status amount, meet following self adaptation and retrain:

${\stackrel{\&CenterDot;}{\mathrm{\&lambda;}}}_1=-a_1{\mathrm{\&lambda;}}_1+g_1{\mathrm{\&Delta;T}}_m$

Wherein a₁For normal number undetermined, g₁For the gain relevant with spool model, Δ T_m=T_m-sat(T_m) it is controller Deviation between the limited input torque of output torque and realistic model；Motor torque saturation function is defined as:

$sat\left(T_m\right)=\left\{\begin{array}{cc}{T}_{mmax}& T_m\&GreaterEqual;T_{mmax}\\ T_m& -T_{mmax}<T_m<T_{mmax}\\ -T_{mmax}& T_m\&le;-T_{mmax}\end{array}\right.$

Make slow sliding formworkDerivative is zero, obtains virtual controlling amount For expecting spool angular speed, Here zero it is set to；

Select exponentially approaching ruleAgain to fast sliding formworkDerivation also makes it be equal to Reaching Law, Finally make the g in the constraint of anti-saturation module self adaptation₁=b₁, obtaining motor control moment is:

Wherein Sliding-mode surface anti-jitter saturation function sat (s) is defined as:

Wherein Δ₁≤10^-3, Δ₂≤10^-4, Δ₁And Δ₂For positive number；

4) platform stance design of control law；

The principle of platform pitch attitude controller is identical with spool moment with design procedure；The definition platform angle of pitch Hurry up, slow loop sliding-mode surface as follows:

Wherein k₃And k₄For positive coefficient undetermined；Ω_θ1=θ_1d-θ₁For the platform angle of pitch instruction and the actual angle of pitch between inclined Difference；For fast loop state deviation；ω_θ1cFor platform angle of pitch virtual controlling amount, by slow loop Equivalent control measure out, For expectation pitch rate, it is set to zero here；λ₂For bowing Elevation angle anti-saturation quantity of state, meets self adaptation and retrains:a₂For normal number undetermined, g₂For with The gain that pitch channel model is relevant；Δτ_c=τ_c-sat(τ_c) be controller output torque with realistic model limited defeated Entering the deviation between moment, platform pitch control moment saturation function is defined as:

$sat\left({\mathrm{\&tau;}}_c\right)=\left\{\begin{array}{cc}{\mathrm{\&tau;}}_{cmax}& {\mathrm{\&tau;}}_c\&GreaterEqual;{\mathrm{\&tau;}}_{cmax}\\ {\mathrm{\&tau;}}_c& -{\mathrm{\&tau;}}_{cmax}<{\mathrm{\&tau;}}_c<{\mathrm{\&tau;}}_{cmax}\\ -{\mathrm{\&tau;}}_{cmax}& {\mathrm{\&tau;}}_c\&le;-{\mathrm{\&tau;}}_{cmax}\end{array}\right.$

Make g₂Equal to b₂, select exponentially approaching rule, then obtaining platform pitching sliding formwork control law is:

Whereink_θ1And ε_θ1For positive count

$\begin{array}{c}f(x,T)=I_1^{-1}\{-I_1{\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&alpha;}}}_1-l_{rt}^{-1}\mathrm{\&lambda;}EA\&lsqb;-x_d\cos (\mathrm{\&beta;}+{\mathrm{\&theta;}}_1)+y_d\sin (\mathrm{\&beta;}+{\mathrm{\&theta;}}_1)\&rsqb;\\ \&CenterDot;\&lsqb;l_{rt}-s-y_d\cos (\mathrm{\&beta;}+{\mathrm{\&theta;}}_1)-x_d\sin (\mathrm{\&beta;}+{\mathrm{\&theta;}}_1)+y_p{\mathrm{cos\&theta;}}_2+x_p{\mathrm{sin\&theta;}}_2\&rsqb;\}\end{array}.$

Compared with prior art, the method have the advantages that

The present invention first derived assembly towing kinetic model.For this model is compared to Mass Model, can To characterize the attitudes vibration of two ends spacecraft；For model compared to consideration spacecraft attitude in the past, not only may be used It is readily adaptable for use in tether relaxation cases being applied to tether tensioning state.Secondly, the winding defining tether is long Degree, this length can be in order to reflect the change under winding of the tether tension force.This only comes with winding angle than external Characterize wrapping phenomena and cannot represent that the change of tension force will be closer to actual sight.In addition this definition is more beneficial for twining Around the research of mechanism, also the theoretical foundation that offer is strong can be proposed strategy antiwind to follow-up anticollision.Finally, Devise spool control law to regulate tether tension force.This specific thrust filtering technique more directly and more initiatively carries out opening Power controls, and nor affects on the application of conventional art simultaneously.Therefore, this control strategy can alleviate platform thrust undoubtedly Burden, also make orbit Design have bigger degree of freedom.

[accompanying drawing explanation]

The towing of Fig. 1 assembly becomes rail areal model

Fig. 2 spool model

Fig. 3 is wound around model

Fig. 4 pulls transfer orbital control device signal diagram

[detailed description of the invention]

Below in conjunction with the accompanying drawings the present invention is described in further detail:

Seeing Fig. 1-Fig. 3, the present invention utilizes the towing that spool controls to become the antiwind collision-proof method of rail, including with Lower step:

1) the assembly change rail kinetic model considering that two ends attitude and tether are lax is set up；

Lagrangian method is utilized to set up assembly orbital plane internal dynamics model:

$\begin{array}{c}{\stackrel{\&CenterDot;\&CenterDot;}{r}}_1=r_1{\stackrel{\&CenterDot;}{\mathrm{\&alpha;}}}_1^2-\frac{\mathrm{\&mu;}}{r_1^2}+\frac{1}{m_1+m_2}\{m_2\stackrel{\&CenterDot;\&CenterDot;}{s}\sin \mathrm{\&beta;}-\frac{3{\mathrm{\&mu;m}}_2{s}^2}{r_1^4}+\frac{9{\mathrm{\&mu;m}}_2{s}^2{\cos }^2\mathrm{\&beta;}}{2r_1^4}\\ +m_2\cos \mathrm{\&beta;}\&lsqb;s({\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&alpha;}}}_1-\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&beta;}})+2\stackrel{\&CenterDot;}{s}({\stackrel{\&CenterDot;}{\mathrm{\&alpha;}}}_1-\stackrel{\&CenterDot;}{\mathrm{\&beta;}})\&rsqb;-m_{2}s\sin \mathrm{\&beta;}{({\stackrel{\&CenterDot;}{\mathrm{\&alpha;}}}_1-\stackrel{\&CenterDot;}{\mathrm{\&beta;}})}^2\\ -\frac{2{\mathrm{\&mu;m}}_{2}s\sin \mathrm{\&beta;}}{r_1^3}+Q_{r1}\}\end{array}$

$\begin{array}{c}{\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&alpha;}}}_1=\frac{1}{m_2(r_1^2+s^2-2{\mathrm{sr}}_1\sin \mathrm{\&beta;})+I_1+I_2+m_1{r}_1^2}\{-2m_2\stackrel{\&CenterDot;}{s}{r}_1\sin \mathrm{\&beta;}(\stackrel{\&CenterDot;}{\mathrm{\&beta;}}-{\stackrel{\&CenterDot;}{\mathrm{\&alpha;}}}_1)\\ +\&lsqb;-I_1{\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&theta;}}}_1-I_2{\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&theta;}}}_2+I_2-m_2({\mathrm{sr}}_1\sin \mathrm{\&beta;}-s^2)\&rsqb;\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&beta;}}-m_2\cos \mathrm{\&beta;}(s{\stackrel{\&CenterDot;\&CenterDot;}{r}}_1+r_1\stackrel{\&CenterDot;\&CenterDot;}{s})\\ -m_{2}s(r_1{\stackrel{\&CenterDot;}{\mathrm{\&beta;}}}^2\cos \mathrm{\&beta;}-2r_1{\stackrel{\&CenterDot;}{\mathrm{\&alpha;}}}_1\stackrel{\&CenterDot;}{\mathrm{\&beta;}}\cos \mathrm{\&beta;}-2{\stackrel{\&CenterDot;}{r}}_1{\stackrel{\&CenterDot;}{\mathrm{\&alpha;}}}_1\sin \mathrm{\&beta;})+m_2{\stackrel{\&CenterDot;}{r}}_1\stackrel{\&CenterDot;}{s}\cos \mathrm{\&beta;}\\ -2m_{2}s\stackrel{\&CenterDot;}{s}({\stackrel{\&CenterDot;}{\mathrm{\&alpha;}}}_1-\stackrel{\&CenterDot;}{\mathrm{\&beta;}})-m_2{r}_1\stackrel{\&CenterDot;}{s}\stackrel{\&CenterDot;}{\mathrm{\&beta;}}\sin \mathrm{\&beta;}-2r_1{\stackrel{\&CenterDot;}{r}}_1{\stackrel{\&CenterDot;}{\mathrm{\&alpha;}}}_1(m_1+m_2)+Q_{\mathrm{\&alpha;}1}\}\end{array}$

$\begin{array}{c}{\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&theta;}}}_1=\frac{1}{I_1}\{Q_{\mathrm{\&theta;}1}-I_1{\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&alpha;}}}_1-l_{rt}^{-1}\mathrm{\&lambda;}EA\&lsqb;-x_d\cos (\mathrm{\&beta;}+{\mathrm{\&theta;}}_1)+y_d\sin (\mathrm{\&beta;}+{\mathrm{\&theta;}}_1)\&rsqb;\\ \&CenterDot;\&lsqb;l_{rt}-s-y_d\cos (\mathrm{\&beta;}+{\mathrm{\&theta;}}_1)-x_d\sin (\mathrm{\&beta;}+{\mathrm{\&theta;}}_1)+y_p{\mathrm{cos\&theta;}}_2+x_p{\mathrm{sin\&theta;}}_2\&rsqb;\}\end{array}$

$\begin{array}{c}\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&beta;}}=\frac{1}{m_2{s}^2+I_2}\{(m_2{s}^2+I_2-m_2{r}_{1}s\sin \mathrm{\&beta;}){\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&alpha;}}}_1+I_2{\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&theta;}}}_2+m_{2}s\cos \mathrm{\&beta;}{\stackrel{\&CenterDot;\&CenterDot;}{r}}_1\\ +2m_{2}s\stackrel{\&CenterDot;}{s}({\stackrel{\&CenterDot;}{\mathrm{\&alpha;}}}_1-\stackrel{\&CenterDot;}{\mathrm{\&beta;}})-l_{rt}^{-1}\mathrm{\&lambda;}EA\&lsqb;-x_d\cos (\mathrm{\&beta;}+{\mathrm{\&theta;}}_1)+y_d\sin (\mathrm{\&beta;}+{\mathrm{\&theta;}}_1)\&rsqb;\\ \&CenterDot;\&lsqb;l_{rt}-s-y_d\cos (\mathrm{\&beta;}+{\mathrm{\&theta;}}_1)-x_d\sin (\mathrm{\&beta;}+{\mathrm{\&theta;}}_1)+y_p{\mathrm{cos\&theta;}}_2+x_p{\mathrm{sin\&theta;}}_2\&rsqb;\\ -2m_{2}s{\stackrel{\&CenterDot;}{\mathrm{\&alpha;}}}_1{\stackrel{\&CenterDot;}{r}}_1\sin \mathrm{\&beta;}+\frac{3{\mathrm{\&mu;m}}_2{s}^2\sin 2\mathrm{\&beta;}}{2r_1^3}+\frac{{\mathrm{\&mu;m}}_{2}s\cos \mathrm{\&beta;}}{r_1^2}-m_2{\mathrm{sr}}_1{\stackrel{\&CenterDot;}{\mathrm{\&alpha;}}}_1^2+Q_{\mathrm{\&beta;}}\}\end{array}$

$\begin{array}{c}\stackrel{\&CenterDot;\&CenterDot;}{s}={\stackrel{\&CenterDot;\&CenterDot;}{r}}_1\sin \mathrm{\&beta;}+r_1{\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&alpha;}}}_1\cos \mathrm{\&beta;}+\frac{1}{m_2}\{m_{2}s{({\stackrel{\&CenterDot;}{\mathrm{\&alpha;}}}_1-\stackrel{\&CenterDot;}{\mathrm{\&beta;}})}^2+\mathrm{\&lambda;}EA(1-\frac{s}{l_{rt}})\\ +2m_2{\stackrel{\&CenterDot;}{\mathrm{\&alpha;}}}_1{\stackrel{\&CenterDot;}{r}}_1\cos \mathrm{\&beta;}-m_2{r}_1{\stackrel{\&CenterDot;}{\mathrm{\&alpha;}}}_1^2\sin \mathrm{\&beta;}+\frac{{\mathrm{\&mu;m}}_{2}s}{2r_1^3}+\frac{{\mathrm{\&mu;m}}_2\sin \mathrm{\&beta;}}{r_1^2}\\ -\frac{3{\mathrm{\&mu;m}}_{2}s\cos 2\mathrm{\&beta;}}{2r_1^3}+l_{rt}^{-1}\mathrm{\&lambda;}EA\&lsqb;-y_d\cos (\mathrm{\&beta;}+{\mathrm{\&theta;}}_1)-x_d\sin (\mathrm{\&beta;}+{\mathrm{\&theta;}}_1)\\ +y_p{\mathrm{cos\&theta;}}_2+x_p{\mathrm{sin\&theta;}}_2\&rsqb;+Q_s\}\end{array}$

$\begin{array}{c}{\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&theta;}}}_2=\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&beta;}}-{\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&alpha;}}}_1+\frac{1}{I_2}\{-l_{rt}^{-1}\mathrm{\&lambda;}EA(x_p{\mathrm{cos\&theta;}}_2-y_p{\mathrm{sin\&theta;}}_2)\&lsqb;l_{rt}-s+y_p{\mathrm{cos\&theta;}}_2\\ -y_d\cos (\mathrm{\&beta;}+{\mathrm{\&theta;}}_1)-x_d\sin (\mathrm{\&beta;}+{\mathrm{\&theta;}}_1)+x_p{\mathrm{sin\&theta;}}_2\&rsqb;+Q_{\mathrm{\&theta;}2}\}\end{array}$

Wherein, q=[r₁,α₁,θ₁,β,s,θ₂]^TFor 6DOF generalized coordinates, r in assembly orbital plane₁Put down for space Platform barycenter orbit radius, α₁For platform barycenter true anomaly, θ₁For platform pitch attitude angle, β is two ends space flight Device barycenter line and local horizontal line angle (that is, face interior angle), s is two ends spacecraft centroid lines, θ₂For mesh Standard type pitch attitude angle, l_rtLong for the rope after deduction coiling length, m₁For platform mass, m₂For objective body quality, I₁For platform pitch rotation inertia, I₂For objective body pitch rotation inertia；λ is tether relaxation factor, and relaxing is 0 Tensioning is 1；EA is tether rigidity；Each generalized force Q_r1、Q_α1、Q_θ1、Q_β、Q_s、Q_θ2Define with tether tension force As follows:

$\left\{\begin{array}{c}{Q}_{r1}=-F{\mathrm{sin\&theta;}}_1\\ Q_{\mathrm{\&alpha;}1}={\mathrm{Fr}}_1{\mathrm{cos\&theta;}}_1\\ Q_{\mathrm{\&theta;}1}={\mathrm{\&tau;}}_c\\ Q_{\mathrm{\&beta;}}=0\\ Q_s=0\\ Q_{\mathrm{\&theta;}2}=0\end{array}\right.T=\left\{\begin{array}{cc}\frac{EA(l-l_{rt})}{l_{rt}}& l>l_{rt}\\ 0& l\&le;l_{rt}\end{array}\right.$

Wherein, F is space platform thrust, τ_cFor platform stance control moment,For tether point of release in space Vector under platform body system,The vector arrested a little under complex for tether,For being referred to by point of release To the tension force vector arrested a little,For by arrest the tension force that points to point of release to；φ is tether and two barycenter company The angle of line, its with deformation after the long l of rope be defined as follows:

Wherein, (x_d,y_d) it is point of release coordinate, (x under platform body system_p,y_p) for arresting a little under complex Coordinate；

2) set up the spool Controlling model of tether and be wound around model；

Tether spool Controlling model:

The moment of momentum theorem is used to set up spool kinetic model as follows:

$I_r{\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&phi;}}}_r+C_d{\stackrel{\&CenterDot;}{\mathrm{\&phi;}}}_r=Tr-T_m$

$r=\sqrt{s_2-s_1{l}_r}$

${\mathrm{\&phi;}}_r=-\frac{2}{S_1}\sqrt{S_2-S_1{l}_r}+\frac{2\sqrt{S_2}}{S_1}$

$S_1=\frac{r_d^2}{w_d}{S}_2=S_1{L}_r+R_1^2$

Wherein, I_rFor spool rotary inertia, φ_rFor spool corner, C_dFor spool damped coefficient, r is spool half Footpath, T_mFor reel motor control moment, l_rNot deformed rope for spool release is long, r_dFor tether diameter, w_dFor Spool width, R₁For without spool radius during tether, L_rLong for spool maximum release rope；

Tether winding model:

Assume initially that the rectangle that space platform is a × b m, objective body and intelligence fly pawl and be considered as an entirety, for the length of side It it is the square of cm；Secondly for space platform from the beginning of the summit on the downside of tether point of release, by side clockwise Number to each summit, be followed successively by 0,1,2,3；For objective body from the beginning of the summit arresting a upside, still by suitable Clockwise carries out summit numbering, is followed successively by 0,1,2,3；When two ends spacecraft and tether occur to be wound around, space flight Tether junction point on device will be moved on corresponding summit, and tether junction point is point of release or arrests a little；

Definition platform winding angle ψ=θ₁+ β-φ, and objective body winding angle η=θ₂-φ, wherein, ψ is tether and this The angle of body wobble shaft negative sense, η is the angle of tether and objective body wobble shaft forward；When they meet following bar During part, then it is assumed that be wound around and occur:

Definition tw is for being wound around coefficient, and cn is for being wound around the number of turns, l_twpFor platform coiling length, l_twdIt is wound around for objective body Length, flag is for being wound around point (summit) sequence number；Wherein cn is expressed as: cn=[tw/4], and [] is rounding operation symbol, And institute's round numbers is less than the number in operator；If point of release is respectively with arresting respective initial coordinate a little (x_d0,y_d0) and (x_p0,y_p0)；

For platform:

For objective body:

Therefore total coiling length is l_tw=l_twp+l_twd, a length of l of not deformed rope of actual deduction coiling length_rt=l_r-l_tw；

3) the spool design of control law of anticollision/winding；

First the tension force after estimating system is stable:

$\hat{T}=\frac{m_{2}F}{m_1+m_2}$

Determine tension restriction scope:

$T_{min}=\frac{1}{2}\hat{T},T_{max}=\frac{3}{2}\hat{T}$

Wherein the tension force upper limit retrains if it exceeds thrust, then set thrust as the tension force upper limit；

Calculating tension restriction equivalence spool corner:

${\mathrm{\&phi;}}_{rd\min }=-\frac{2}{S_1}\sqrt{S_2-S_1(\frac{l}{1+T_{\min }/EA}+l_{tw})}+\frac{2\sqrt{S_2}}{S_1}$

${\mathrm{\&phi;}}_{rdmax}=-\frac{2}{S_1}\sqrt{S_2-S_1(\frac{l}{1+T_{\max }/EA}+l_{tw})}+\frac{2\sqrt{S_2}}{S_1}$

Calculating spool corner tracking error:

${\mathrm{\&Omega;}}_r=\left\{\begin{array}{cc}{\mathrm{\&phi;}}_{rdmax}-{\mathrm{\&phi;}}_r& T\&GreaterEqual;T_{max}\\ {\stackrel{\&CenterDot;}{\mathrm{\&phi;}}}_r& T_{\min }<T<T_{max}\\ {\mathrm{\&phi;}}_{rd\min }-{\mathrm{\&phi;}}_r& T\&le;T_{\min }\end{array}\right.$

Wherein tension force uses and triggers control strategy, just carries out tension force control time outside only tether tension force is in constraint System, then maintains the long holding of rope constant within it is in restriction range, allows tension force freely change；

The speed sliding-mode surface of definition spool corner is:

Wherein k₁And k₂For normal number,For fast Sliding Mode Track deviation, ω_rcFor the virtual control of corner speed Amount processed is pushed away by slow sliding formwork Equivalent control law, λ₁For anti-saturation module status amount, meet following self adaptation and retrain:

${\stackrel{\&CenterDot;}{\mathrm{\&lambda;}}}_1=-a_1{\mathrm{\&lambda;}}_1+g_1{\mathrm{\&Delta;T}}_m$

Wherein a₁For normal number undetermined, g₁For the gain relevant with spool model, Δ T_m=T_m-sat(T_m) it is controller Deviation between the limited input torque of output torque and realistic model；Motor torque saturation function is defined as:

$sat\left(T_m\right)=\left\{\begin{array}{cc}{T}_{mmax}& T_m\&GreaterEqual;T_{mmax}\\ T_m& -T_{mmax}<T_m<T_{mmax}\\ -T_{mmax}& T_m\&le;-T_{mmax}\end{array}\right.$

Make slow sliding formworkDerivative is zero, obtains virtual controlling amount For expecting spool angular speed, Here zero it is set to；

Select exponentially approaching ruleAgain to fast sliding formworkDerivation also makes it be equal to Reaching Law, Finally make the g in the constraint of anti-saturation module self adaptation₁=b₁, obtaining motor control moment is:

Wherein Sliding-mode surface anti-jitter saturation function sat (s) is defined as:

Wherein Δ₁≤10^-3, Δ₂≤10^-4, Δ₁And Δ₂For positive number；

4) platform stance design of control law；

The principle of platform pitch attitude controller is identical with spool moment with design procedure；The definition platform angle of pitch Hurry up, slow loop sliding-mode surface as follows:

Wherein k₃And k₄For positive coefficient undetermined；Ω_θ1=θ_1d-θ₁For the platform angle of pitch instruction and the actual angle of pitch between inclined Difference；For fast loop state deviation；ω_θ1cFor platform angle of pitch virtual controlling amount, by slow loop Equivalent control measure out, For expectation pitch rate, it is set to zero here；λ₂For bowing Elevation angle anti-saturation quantity of state, meets self adaptation and retrains:a₂For normal number undetermined, g₂For with The gain that pitch channel model is relevant；Δτ_c=τ_c-sat(τ_c) be controller output torque with realistic model limited defeated Entering the deviation between moment, platform pitch control moment saturation function is defined as:

$sat\left({\mathrm{\&tau;}}_c\right)=\left\{\begin{array}{cc}{\mathrm{\&tau;}}_{cmax}& {\mathrm{\&tau;}}_c\&GreaterEqual;{\mathrm{\&tau;}}_{cmax}\\ {\mathrm{\&tau;}}_c& -{\mathrm{\&tau;}}_{cmax}<{\mathrm{\&tau;}}_c<{\mathrm{\&tau;}}_{cmax}\\ -{\mathrm{\&tau;}}_{cmax}& {\mathrm{\&tau;}}_c\&le;-{\mathrm{\&tau;}}_{cmax}\end{array}\right.$

Make g₂Equal to b₂, select exponentially approaching rule, then obtaining platform pitching sliding formwork control law is:

Whereink_θ1And ε_θ1For positive count

$\begin{array}{c}f(x,T)=I_1^{-1}\{-I_1{\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&alpha;}}}_1-l_{rt}^{-1}\mathrm{\&lambda;}EA\&lsqb;-x_d\cos (\mathrm{\&beta;}+{\mathrm{\&theta;}}_1)+y_d\sin (\mathrm{\&beta;}+{\mathrm{\&theta;}}_1)\&rsqb;\\ \&CenterDot;\&lsqb;l_{rt}-s-y_d\cos (\mathrm{\&beta;}+{\mathrm{\&theta;}}_1)-x_d\sin (\mathrm{\&beta;}+{\mathrm{\&theta;}}_1)+y_p{\mathrm{cos\&theta;}}_2+x_p{\mathrm{sin\&theta;}}_2\&rsqb;\}\end{array}.$

Above content is only the technological thought that the present invention is described, it is impossible to limit protection scope of the present invention with this, all It is the technological thought proposed according to the present invention, any change done on the basis of technical scheme, each fall within this Within the protection domain of bright claims.

Claims (1)

1. the towing that a kind utilizes spool to control becomes the antiwind collision-proof method of rail, it is characterised in that include following Step:

1) the assembly change rail kinetic model considering that two ends attitude and tether are lax is set up；

Lagrangian method is utilized to set up assembly orbital plane internal dynamics model:

$\begin{array}{c}{\stackrel{\&CenterDot;\&CenterDot;}{r}}_1=r_1{\stackrel{\&CenterDot;}{\mathrm{\&alpha;}}}_1^2-\frac{\mathrm{\&mu;}}{r_1^2}+\frac{1}{m_1+m_2}\{m_2\stackrel{\&CenterDot;\&CenterDot;}{s}\sin \mathrm{\&beta;}-\frac{3{\mathrm{\&mu;m}}_2{s}^2}{r_1^4}+\frac{9{\mathrm{\&mu;m}}_2{s}^2{\cos }^2\mathrm{\&beta;}}{2r_1^4}\\ +m_2\cos \mathrm{\&beta;}\&lsqb;s({\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&alpha;}}}_1-\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&beta;}})+2\stackrel{\&CenterDot;}{s}({\stackrel{\&CenterDot;}{\mathrm{\&alpha;}}}_1-\stackrel{\&CenterDot;}{\mathrm{\&beta;}})\&rsqb;-m_{2}s\sin \mathrm{\&beta;}{({\stackrel{\&CenterDot;}{\mathrm{\&alpha;}}}_1-\stackrel{\&CenterDot;}{\mathrm{\&beta;}})}^2\\ -\frac{2{\mathrm{\&mu;m}}_{2}s\sin \mathrm{\&beta;}}{r_1^3}+Q_{r1}\}\end{array}$

$\begin{array}{c}{\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&alpha;}}}_1=\frac{1}{m_2(r_1^2+s^2-2{\mathrm{sr}}_1\sin \mathrm{\&beta;})+I_1+I_2+m_1{r}_1^2}\{-2m_2\stackrel{\&CenterDot;}{s}{r}_1\sin \mathrm{\&beta;}(\stackrel{\&CenterDot;}{\mathrm{\&beta;}}-{\stackrel{\&CenterDot;}{\mathrm{\&alpha;}}}_1)\\ +\&lsqb;-I_1{\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&theta;}}}_1-I_2{\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&theta;}}}_2+I_2-m_2({\mathrm{sr}}_1\sin \mathrm{\&beta;}-s^2)\&rsqb;\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&beta;}}-m_2\cos \mathrm{\&beta;}(s{\stackrel{\&CenterDot;\&CenterDot;}{r}}_1+r_1\stackrel{\&CenterDot;\&CenterDot;}{s})\\ -m_{2}s(r_1{\stackrel{\&CenterDot;}{\mathrm{\&beta;}}}^2\cos \mathrm{\&beta;}-2r_1{\stackrel{\&CenterDot;}{\mathrm{\&alpha;}}}_1\stackrel{\&CenterDot;}{\mathrm{\&beta;}}\cos \mathrm{\&beta;}-2{\stackrel{\&CenterDot;}{r}}_1{\stackrel{\&CenterDot;}{\mathrm{\&alpha;}}}_1\sin \mathrm{\&beta;})+m_2{\stackrel{\&CenterDot;}{r}}_1\stackrel{\&CenterDot;}{s}\cos \mathrm{\&beta;}\\ -2m_{2}s\stackrel{\&CenterDot;}{s}({\stackrel{\&CenterDot;}{\mathrm{\&alpha;}}}_1-\stackrel{\&CenterDot;}{\mathrm{\&beta;}})-m_2{r}_1\stackrel{\&CenterDot;}{s}\stackrel{\&CenterDot;}{\mathrm{\&beta;}}\sin \mathrm{\&beta;}-2r_1{\stackrel{\&CenterDot;}{r}}_1{\stackrel{\&CenterDot;}{\mathrm{\&alpha;}}}_1(m_1+m_2)+Q_{\mathrm{\&alpha;}1}\}\end{array}$

$\begin{array}{c}{\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&theta;}}}_1=\frac{1}{I_1}\{Q_{\mathrm{\&theta;}1}-I_1{\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&alpha;}}}_1-l_{rt}^{-1}\mathrm{\&lambda;}EA\&lsqb;-x_d\cos (\mathrm{\&beta;}+{\mathrm{\&theta;}}_1)+y_d\sin (\mathrm{\&beta;}+{\mathrm{\&theta;}}_1)\&rsqb;\\ \&CenterDot;\&lsqb;l_{rt}-s-y_d\cos (\mathrm{\&beta;}+{\mathrm{\&theta;}}_1)-x_d\sin (\mathrm{\&beta;}+{\mathrm{\&theta;}}_1)+y_p{\mathrm{cos\&theta;}}_2+x_p{\mathrm{sin\&theta;}}_2\&rsqb;\}\end{array}$

$\begin{array}{c}\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&beta;}}=\frac{1}{m_2{s}^2+I_2}\{(m_2{s}^2+I_2-m_2{r}_{1}s\sin \mathrm{\&beta;}){\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&alpha;}}}_1+I_2{\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&theta;}}}_2+m_{2}s\cos \mathrm{\&beta;}{\stackrel{\&CenterDot;\&CenterDot;}{r}}_1\\ +2m_{2}s\stackrel{\&CenterDot;}{s}({\stackrel{\&CenterDot;}{\mathrm{\&alpha;}}}_1-\stackrel{\&CenterDot;}{\mathrm{\&beta;}})-l_{rt}^{-1}\mathrm{\&lambda;}EA\&lsqb;-x_d\cos (\mathrm{\&beta;}+{\mathrm{\&theta;}}_1)+y_d\sin (\mathrm{\&beta;}+{\mathrm{\&theta;}}_1)\&rsqb;\\ \&CenterDot;\&lsqb;l_{rt}-s-y_d\cos (\mathrm{\&beta;}+{\mathrm{\&theta;}}_1)-x_d\sin (\mathrm{\&beta;}+{\mathrm{\&theta;}}_1)+y_p{\mathrm{cos\&theta;}}_2+x_p{\mathrm{sin\&theta;}}_2\&rsqb;\\ -2m_{2}s{\stackrel{\&CenterDot;}{\mathrm{\&alpha;}}}_1{\stackrel{\&CenterDot;}{r}}_1\sin \mathrm{\&beta;}+\frac{3{\mathrm{\&mu;m}}_2{s}^2\sin 2\mathrm{\&beta;}}{2r_1^3}+\frac{{\mathrm{\&mu;m}}_{2}s\cos \mathrm{\&beta;}}{r_1^2}-m_2{\mathrm{sr}}_1{\stackrel{\&CenterDot;}{\mathrm{\&alpha;}}}_1^2+Q_{\mathrm{\&beta;}}\}\end{array}$

$\begin{array}{c}\stackrel{\&CenterDot;\&CenterDot;}{s}={\stackrel{\&CenterDot;\&CenterDot;}{r}}_1\sin \mathrm{\&beta;}+r_1{\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&alpha;}}}_1\cos \mathrm{\&beta;}+\frac{1}{m_2}\{m_{2}s{({\stackrel{\&CenterDot;}{\mathrm{\&alpha;}}}_1-\stackrel{\&CenterDot;}{\mathrm{\&beta;}})}^2+\mathrm{\&lambda;}EA(1-\frac{s}{l_{rt}})\\ +2m_2{\stackrel{\&CenterDot;}{\mathrm{\&alpha;}}}_1{\stackrel{\&CenterDot;}{r}}_1\cos \mathrm{\&beta;}-m_2{r}_1{\stackrel{\&CenterDot;}{\mathrm{\&alpha;}}}_1^2\sin \mathrm{\&beta;}+\frac{{\mathrm{\&mu;m}}_{2}s}{2r_1^3}+\frac{{\mathrm{\&mu;m}}_2\sin \mathrm{\&beta;}}{r_1^2}\\ -\frac{3{\mathrm{\&mu;m}}_{2}s\cos 2\mathrm{\&beta;}}{2r_1^3}+l_{rt}^{-1}\mathrm{\&lambda;}EA\&lsqb;-y_d\cos (\mathrm{\&beta;}+{\mathrm{\&theta;}}_1)-x_d\sin (\mathrm{\&beta;}+{\mathrm{\&theta;}}_1)\\ +y_p{\mathrm{cos\&theta;}}_2+x_p{\mathrm{sin\&theta;}}_2\&rsqb;+Q_s\}\end{array}$

$\begin{array}{c}{\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&theta;}}}_2=\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&beta;}}-{\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&alpha;}}}_1+\frac{1}{I_2}\{-l_{rt}^{-1}\mathrm{\&lambda;}EA(x_p{\mathrm{cos\&theta;}}_2-y_p{\mathrm{sin\&theta;}}_2)\&lsqb;l_{rt}-s+y_p{\mathrm{cos\&theta;}}_2\\ -y_d\cos (\mathrm{\&beta;}+{\mathrm{\&theta;}}_1)-x_d\sin (\mathrm{\&beta;}+{\mathrm{\&theta;}}_1)+x_p{\mathrm{sin\&theta;}}_2\&rsqb;+Q_{\mathrm{\&theta;}2}\}\end{array}$

Wherein, q=[r₁,α₁,θ₁,β,s,θ₂]^TFor 6DOF generalized coordinates, r in assembly orbital plane₁Put down for space Platform barycenter orbit radius, α₁For platform barycenter true anomaly, θ₁For platform pitch attitude angle, β is two ends space flight Device barycenter line and local horizontal line angle, s is two ends spacecraft centroid lines, θ₂For objective body pitch attitude Angle, l_rtLong for the rope after deduction coiling length, m₁For platform mass, m₂For objective body quality, I₁Bow for platform Face upward rotary inertia, I₂For objective body pitch rotation inertia；λ is tether relaxation factor, relax be 0 tensioning be 1； EA is tether rigidity；Each generalized force Q_r1、Q_α1、Q_θ1、Q_β、Q_s、Q_θ2It is defined as follows with tether tension force:

$\begin{array}{cc}\left\{\begin{array}{c}{Q}_{r1}=-F{\mathrm{sin\&theta;}}_1\\ Q_{\mathrm{\&alpha;}1}={\mathrm{Fr}}_1{\mathrm{cos\&theta;}}_1\\ Q_{\mathrm{\&theta;}1}={\mathrm{\&tau;}}_c\\ Q_{\mathrm{\&beta;}}=0\\ Q_s=0\\ Q_{\mathrm{\&theta;}2}=0\end{array}\right.& T=\left\{\begin{array}{cc}\frac{EA(l-l_{rt})}{l_{rt}}& l>l_{rt}\\ 0& l\&le;l_{rt}\end{array}\right.\end{array}$

Wherein, F is space platform thrust, τ_cFor platform stance control moment,For tether point of release in space Vector under platform body system,The vector arrested a little under complex for tether,For being referred to by point of release To the tension force vector arrested a little,For by arrest the tension force that points to point of release to；φ is tether and two barycenter company The angle of line, its with deformation after the long l of rope be defined as follows:

Wherein, (x_d,y_d) it is point of release coordinate, (x under platform body system_p,y_p) for arresting a little under complex Coordinate；

2) set up the spool Controlling model of tether and be wound around model；

Tether spool Controlling model:

The moment of momentum theorem is used to set up spool kinetic model as follows:

$I_r{\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&phi;}}}_r+C_d{\stackrel{\&CenterDot;}{\mathrm{\&phi;}}}_r=Tr-T_m$

$r=\sqrt{s_2-s_1{l}_r}$

${\mathrm{\&phi;}}_r=-\frac{2}{S_1}\sqrt{S_2-S_1{l}_r}+\frac{2\sqrt{S_2}}{S_1}$

$\begin{array}{cc}{S}_1=\frac{r_d^2}{w_d}& S_2=S_1{L}_r+R_1^2\end{array}$

Wherein, I_rFor spool rotary inertia, φ_rFor spool corner, C_dFor spool damped coefficient, r is spool half Footpath, T_mFor reel motor control moment, l_rNot deformed rope for spool release is long, r_dFor tether diameter, w_dFor Spool width, R₁For without spool radius during tether, L_rLong for spool maximum release rope；

Tether winding model:

Assume initially that the rectangle that space platform is a × b m, objective body and intelligence fly pawl and be considered as an entirety, for the length of side It it is the square of c m；Secondly for space platform from the beginning of the summit on the downside of tether point of release, by side clockwise Number to each summit, be followed successively by 0,1,2,3；For objective body from the beginning of the summit arresting a upside, still by suitable Clockwise carries out summit numbering, is followed successively by 0,1,2,3；When two ends spacecraft and tether occur to be wound around, space flight Tether junction point on device will be moved on corresponding summit, and tether junction point is point of release or arrests a little；

Definition platform winding angle ψ=θ₁+ β-φ, and objective body winding angle η=θ₂-φ, wherein, ψ is tether and this The angle of body wobble shaft negative sense, η is the angle of tether and objective body wobble shaft forward；When they meet following bar During part, then it is assumed that be wound around and occur:

Definition tw is for being wound around coefficient, and cn is for being wound around the number of turns, l_twpFor platform coiling length, l_twdIt is wound around for objective body Length, flag is for being wound around point (summit) sequence number；Wherein cn is expressed as: cn=[tw/4], and [] is rounding operation symbol, And institute's round numbers is less than the number in operator；If point of release is respectively with arresting respective initial coordinate a little (x_d0,y_d0) and (x_p0,y_p0)；

For platform:

For objective body:

Therefore total coiling length is l_tw=l_twp+l_twd, a length of l of not deformed rope of actual deduction coiling length_rt=l_r-l_tw；

3) the spool design of control law of anticollision/winding；

First the tension force after estimating system is stable:

$\hat{T}=\frac{m_{2}F}{m_1+m_2}$

Determine tension restriction scope:

$\begin{array}{cc}{T}_{min}=\frac{1}{2}\hat{T},& T_{max}=\frac{3}{2}\hat{T}\end{array}$

Wherein the tension force upper limit retrains if it exceeds thrust, then set thrust as the tension force upper limit；

Calculating tension restriction equivalence spool corner:

${\mathrm{\&phi;}}_{rd\min }=-\frac{2}{S_1}\sqrt{S_2-S_1(\frac{l}{1+T_{\min }/EA}+l_{tw})}+\frac{2\sqrt{S_2}}{S_1}$

${\mathrm{\&phi;}}_{rdmax}=-\frac{2}{S_1}\sqrt{S_2-S_1(\frac{l}{1+T_{\max }/EA}+l_{tw})}+\frac{2\sqrt{S_2}}{S_1}$

Calculating spool corner tracking error:

${\mathrm{\&Omega;}}_r=\left\{\begin{array}{cc}{\mathrm{\&phi;}}_{rdmax}-{\mathrm{\&phi;}}_r& T\&GreaterEqual;T_{max}\\ {\stackrel{\&CenterDot;}{\mathrm{\&phi;}}}_r& T_{\min }<T<T_{max}\\ {\mathrm{\&phi;}}_{rd\min }-{\mathrm{\&phi;}}_r& T\&le;T_{\min }\end{array}\right.$

Wherein tension force uses and triggers control strategy, just carries out tension force control time outside only tether tension force is in constraint System, then maintains the long holding of rope constant within it is in restriction range, allows tension force freely change；

The speed sliding-mode surface of definition spool corner is:

Wherein k₁And k₂For normal number,For fast Sliding Mode Track deviation, ω_rcFor the virtual control of corner speed Amount processed is pushed away by slow sliding formwork Equivalent control law, λ₁For anti-saturation module status amount, meet following self adaptation and retrain:

${\stackrel{\&CenterDot;}{\mathrm{\&lambda;}}}_1=-a_1{\mathrm{\&lambda;}}_1+g_1{\mathrm{\&Delta;T}}_m$

Wherein a₁For normal number undetermined, g₁For the gain relevant with spool model, Δ T_m=T_m-sat(T_m) it is controller Deviation between the limited input torque of output torque and realistic model；Motor torque saturation function is defined as:

$sat\left(T_m\right)=\left\{\begin{array}{cc}{T}_{mmax}& T_m\&GreaterEqual;T_{mmax}\\ T_m& -T_{mmax}<T_m<T_{mmax}\\ -T_{mmax}& T_m\&le;-T_{mmax}\end{array}\right.$

Make slow sliding formworkDerivative is zero, obtains virtual controlling amount For expecting spool angular speed, Here zero it is set to；

Select exponentially approaching ruleAgain to fast sliding formworkDerivation also makes it be equal to Reaching Law, Finally make the g in the constraint of anti-saturation module self adaptation₁=b₁, obtaining motor control moment is:

WhereinSliding-mode surface anti-jitter saturation function sat (s) is defined as:

Wherein Δ₁≤10^-3, Δ₂≤10^-4, Δ₁And Δ₂For positive number；

4) platform stance design of control law；

The principle of platform pitch attitude controller is identical with spool moment with design procedure；The definition platform angle of pitch Hurry up, slow loop sliding-mode surface as follows:

Wherein k₃And k₄For positive coefficient undetermined；Ω_θ1=θ_1d-θ₁For the platform angle of pitch instruction and the actual angle of pitch between inclined Difference；For fast loop state deviation；ω_θ1cFor platform angle of pitch virtual controlling amount, by slow loop Equivalent control measure out, For expectation pitch rate, it is set to zero here；λ₂For bowing Elevation angle anti-saturation quantity of state, meets self adaptation and retrains:a₂For normal number undetermined, g₂For with The gain that pitch channel model is relevant；Δτ_c=τ_c-sat(τ_c) be controller output torque with realistic model limited defeated Entering the deviation between moment, platform pitch control moment saturation function is defined as:

$sat\left({\mathrm{\&tau;}}_c\right)=\left\{\begin{array}{cc}{\mathrm{\&tau;}}_{cmax}& {\mathrm{\&tau;}}_c\&GreaterEqual;{\mathrm{\&tau;}}_{cmax}\\ {\mathrm{\&tau;}}_c& -{\mathrm{\&tau;}}_{cmax}<{\mathrm{\&tau;}}_c<{\mathrm{\&tau;}}_{cmax}\\ -{\mathrm{\&tau;}}_{cmax}& {\mathrm{\&tau;}}_c\&le;-{\mathrm{\&tau;}}_{cmax}\end{array}\right.$

Make g₂Equal to b₂, select exponentially approaching rule, then obtaining platform pitching sliding formwork control law is:

Whereink_θ1And ε_θ1For positive count

$\begin{array}{c}f(x,T)=I_1^{-1}\{{-I}_1{\stackrel{..}{a}}_1-l_{\mathrm{rt}}^{-1}\mathrm{\&lambda;EA}[{-x}_d\cos (\mathrm{\&beta;}+{\mathrm{\&theta;}}_1)+y_d\sin (\mathrm{\&beta;}+{\mathrm{\&theta;}}_1)\\ \&CenterDot;[l_{\mathrm{rt}}-s-y_d\cos (\mathrm{\&beta;}+{\mathrm{\&theta;}}_1)-x_d\sin (\mathrm{\&beta;}+{\mathrm{\&theta;}}_1)+y_p\cos {\mathrm{\&theta;}}_2+x_p\sin {\mathrm{\&theta;}}_2]\}\end{array}$