CN103064420A - Approaching posture coordination control method of space tether robot with movable tether point - Google Patents

Abstract

The invention relates to an approaching posture coordination control method of a space tether robot with a movable tether point. The method is characterized in that a tether control mechanism is designed, the position of the tether point is controlled through changes of lengths of la, lb and lc, and therefore the direction of pull force is changed and further posture control torque generated by the tether pull force is changed. As to the posture control problem, a controller in a sliding mode variable structure is designed for calculating the needed control torque, then a thruster of the space tether robot is used for providing a control torque on the rolling direction, then the position of the tether point is controlled through control of the lengths of three tethers, and therefore the needed control torque is generated. Compared with approaching control of a traditional space tether robot, the method has the advantages that the designed tether control mechanism is relatively simple and easy to achieve, fuel is effectively saved, and coordination control for positions and postures is achieved at the same time.

Description

The space of removable tether point rope be robot approach the attitude harmony control method

Technical field

The present invention relates to a kind of Spacecraft Control technical research field that belongs to, the space rope that relates to a kind of low fuel consumption is robot tether and thruster attitude harmony control method, this control method can be widely used in the space restrict be robot in the target approaches.

Background technology

Rope be robot since its flexibly, the characteristics such as safety, fuel consumption is low, widely effect is arranged in On-orbit servicing, can carry out inert satellite relief, space trash cleaning, auxiliaryly become the operation such as rail.Be the prerequisite task of carrying out in the rail service to stable the approaching of target, and the position in the approximate procedure and attitude control are that rope is that robot mainly one of is studied.The space rope is that robot discharges backward target approaches from platform, in the process of approaching, need to be according to the attitude needs of the relative measurement sensors such as vision, self attitude is adjusted in real time, because the space rope is that robot self fuel is limited, the attitude control method that designs a kind of fuel saving is very necessary, and it becomes rope is robot field's research emphasis.

Summary of the invention

The technical matters that solves

For fear of the deficiencies in the prior art part, the space rope that the present invention proposes a kind of removable tether point be robot approach the attitude harmony control method, be a kind of suitable space rope be the tether control gear of robot and low fuel consumption to target approaches attitude harmony control method.

Technical scheme

A kind of space rope based on removable tether point be robot approach the attitude harmony control method, it is characterized in that step is as follows:

Step 1: the space rope is that the rear end face of robot has three tether l _a, l _bAnd l _c, three tether l _a, l _bAnd l _cBe connected in tether point t, and tether point position must be positioned at the equilateral triangle that a, b and c consist of, the tether that is connected with platform is connected in the t point, and wherein: a, b and c are that the space restricts is that the rear end face of robot has three tether folding and unfolding mouths; Be under the robot body coordinate system at the space rope thus, a point position is [d 0 h] ^T, b point position is

C point position is

Tether point t is p=[d y _cz _c] T, y _cAnd z _cBe y direction and the z durection component of p, d be barycenter to the distance of rear end face, h be a, b or c to the distance in the rear end face center of circle, three tether length are:

$\left\{\begin{array}{c}{l}_a=\sqrt{y_c^2+{(z_c-h)}^2}\\ l_b=\sqrt{{(y_c-\frac{\sqrt{3}}{2}h)}^2+{(z_c+\frac{1}{2}h)}^2}\\ l_c=\sqrt{{(y_c+\frac{\sqrt{3}}{2}h)}^2+{(z_c+\frac{1}{2}h)}^2}\end{array}\right.;$

Step 2: design based on the attitude controller of sliding moding structure is $T_c={\mathrm{\ω}}^{\×}\mathrm{J\ω}+J{\stackrel{\·}{\mathrm{\ω}}}_d-\mathrm{cJG}\left({\mathrm{\σ}}_e\right){\mathrm{\ω}}_e-\mathrm{\λsgn}\left(s\right),$ Wherein: ω be space rope be robot with respect to the component of inertial coordinates system Space Angle speed under body coordinate system, ω is by dynamics/kinematical equation $\left\{\begin{array}{c}J\stackrel{\·}{\mathrm{\ω}}={-\mathrm{\ω}}^{\×}\mathrm{J\ω}+T_c+T_l\\ \stackrel{\·}{\mathrm{\σ}}=G\left(\mathrm{\σ}\right)\mathrm{\ω}\end{array}\right.$ Obtain;

With

The derivative to the time of difference ω and correction rodrigue parameters σ, J are that the space rope is the moment of inertia matrix of the positive definite symmetry of robot, ω ^*Antisymmetric matrix for the vector multiplication cross computing ${\mathrm{\ω}}^{\×}=\left(\begin{array}{ccc}0& {-\mathrm{\ω}}_3& {\mathrm{\ω}}_2\\ {\mathrm{\ω}}_3& 0& {-\mathrm{\ω}}_1\\ -{\mathrm{\ω}}_2& {\mathrm{\ω}}_1& 0\end{array}\right),$ ω ₁, ω ₂And ω ₃Be three components of ω, T _cFor the space rope is the control moment of robot self attitude coutrol mechanism, and inequality constrain is arranged: | T _c|≤| T _Cmax|; T _lBe the control moment that tether produces, function G (σ) is defined as follows: $G\left(\mathrm{\σ}\right)=\frac{1}{4}[(1-{\mathrm{\σ}}^T\mathrm{\σ})I+{2\mathrm{\σ}}^{\×}+{2\mathrm{\σ\σ}}^T],$ σ ^TBe the transposition of σ, I is 3 * 3 vector of unit length, σ ^*Antisymmetric matrix for the vector multiplication cross computing ${\mathrm{\σ}}^{\×}=\left(\begin{array}{ccc}0& {-\mathrm{\σ}}_3& {\mathrm{\σ}}_2\\ {\mathrm{\σ}}_3& 0& {-\mathrm{\σ}}_1\\ -{\mathrm{\σ}}_2& {\mathrm{\σ}}_1& 0\end{array}\right);$ σ _dBe expectation attitude, ω _dExpect angular velocity under the body series; Attitude Tracking error σ _eWith angular velocity error ω _eBy the error dynamics equation $\left\{\begin{array}{c}J{\stackrel{\·}{\mathrm{\ω}}}_e+J{\stackrel{\·}{\mathrm{\ω}}}_d+{\mathrm{\ω}}^{\×}\mathrm{J\ω}=T_c\\ {\stackrel{\·}{\mathrm{\σ}}}_e=G\left({\mathrm{\σ}}_e\right){\mathrm{\ω}}_e\end{array}\right.$ Obtain,

With

Be respectively ω _e, σ _eAnd ω _dDerivative to the time; S=ω _e+ c σ _eBe sliding hyperplane, parameter c＞0,

Be sign function;

Step 3: control moment T _cThe y durection component and the z durection component by the realization of control tether point position, tether point in the position of rear end face is: $\left\{\begin{array}{c}{z}_c=(T_{\mathrm{cy}}+{\mathrm{dF}}_{\mathrm{lbz}})/F_{\mathrm{lbx}}\\ y_c=({\mathrm{dF}}_{\mathrm{lby}}-T_{\mathrm{cz}})/F_{\mathrm{lbx}}\end{array}\right.;$

Wherein: T _CyAnd T _CzBe the control moment T that calculates in the step 2 _cThe y direction and the component of z direction, F _Lbx, F _LbyAnd F _LbzBe respectively the tether tensile force f _lRope is the component of robot body coordinate x direction in the space;

The equilateral triangle that tether point position is positioned at a, b and c formation, satisfy following constraint condition:

$\left\{\begin{array}{c}{y}_{c\min }\≤y_c\≤y_{c\max }\\ z_{c\min }\≤z_c\≤z_{c\max }\end{array}\right.$

Y wherein _Cmin, y _Cmax, z _CminAnd z _CmaxBe respectively tether point position y _cAnd z _cThe bound of moving area, by the determining positions of three tether folding and unfolding mouth a, b and the c of design;

Control moment T _cX durection component T _CxBe that the thruster of robot self provides by space rope, satisfy constraint condition | T _Cx|≤| T _Cxmax|, T _CxmaxFor the space rope is the Maximum controlling moment of the x of robot direction;

Step 4: provide the control moment of y direction and z direction by the adjustment of the tether point position in the step 3, the control moment of x direction is that robot self thruster provides by the space rope, has realized to the space rope being the coordination control of robot pose.

Beneficial effect

The space of a kind of removable tether point that the present invention proposes restrict be robot approach the attitude harmony control method, with the Traditional Space rope be that robot approaches control ratio following good effect is arranged:

1, the tether control gear of design is compared simply, realizes than being easier to.This tether mechanism only need to control the length of three tethers, thereby reaches the purpose of control.

2, the control method for coordinating that designs is fuel saving effectively.The Traditional Space rope is that the control of robot all is to rely on the thruster of self to realize, and the present invention has introduced tether and thruster is coordinated to control, and has reached the purpose of fuel saving.

3, can reach simultaneously the coordination of position and attitude control.The present invention can utilize this method that attitude is controlled when tether is to position co-ordination control, and traditional coordination is controlled at when utilizing tether that the position is controlled, the time disturbance torque that tether produces attitude.

Description of drawings

Fig. 1 is the synoptic diagram of tether control gear

Fig. 2 is that the space rope is that robot is to the target approaches synoptic diagram

Fig. 3 is that the space rope is that robot approaches the coordination control block diagram

Embodiment

Now in conjunction with the embodiments, the invention will be further described for accompanying drawing:

Embodiments of the invention can be achieved through the following technical solutions:

1, designed tether control gear as shown in Figure 1, by changing l _a, l _b, l _cLength reach the position of control tether point, thereby the direction that changes pulling force changes the attitude control moment of tether pulling force generation.

2, for attitude control problem, at first designed Sliding Mode Controller, calculate needed control moment (formula 14), then utilizing the space rope is the control moment that robot self thruster provides the lift-over direction, then by controlling the length of three tethers, the position (formula 16) of control tether point, thus needed control moment produced.

The space rope is that approaching of robot coordinated design and the attitude controller design two large divisions content that control mainly comprises the tether control gear, and lower mask body is described the present invention in detail:

The space rope is that robot target approaches attitude harmony control, it is characterized by: at first, carry out attitude control in order to utilize the tether pulling force, designed a kind of tether control gear; Then designed the attitude harmony control method of tether and thruster according to the characteristics of said mechanism.Can only provide the attitude of both direction control moment owing to by the tether control gear tether being controlled, therefore designed attitude controller by the sliding moding structure method here, utilize tether that the control moment of both direction is provided, the control moment of another direction is that robot self provides by the space rope.

The tether control gear is that the rear end face of robot has three tether folding and unfolding mouth a, b, c at space rope as shown in Figure 1, by inner tether control motor to three tether l _a, l _b, l _cControl, and three tether l _a, l _b, l _cLink together, tether point is t, and the tether that is connected with platform is connected in the t point, with l _a, l _b, l _cLink together.In approximate procedure, by to l _a, l _b, l _cArticle three, the length of tether control, thus control t point changes the control moment of tether then in the position of rear end face (three bar tether is in tensioned state, thereby guarantees that three tethers are close to rear section), reaches the control to 2 direction attitudes.

During the control attitude, tether l _a, l _b, l _cFor tightening, being close to the space rope is the robot rear end face; The tether that is connected with space platform can provide the pulling force that the tether direction can be provided.

As shown in Figure 2, wherein 1 is space platform, is used for carrying and the emission space rope is robot, and 2 to restrict for the space be robot, and 3 is target, is positioned at the Oxyz coordinate origin, coordinate system O _bx _by _bz _bBe the target body series.

If [x _ry _rz _r] ^T∈ R ³For the space rope is the position of robot under target-based coordinate system, n is orbit averaging angular velocity, [x _py _pz _p] ^T∈ R ³Be space platform position, [F _LxF _LyF _Lz] ∈ R ³Be tether three axle pulling force, mr is that the space rope is the robot quality.

The rope point of setting up departments is that the lower position of robot body coordinate is p=[d y at the space rope _cz _c] ^T, wherein d be barycenter to the distance of rear end face, remain unchanged, and the tether point can freely change at rear end face.Suppose that a, b, 3 lines of c form equilateral triangle, a point position is [d 0 h] ^T, b point position is

C point position is

H is that a, b or c are to the distance in the rear end face center of circle.Then the length of three tethers is respectively:

$\left\{\begin{array}{c}{l}_a=\sqrt{{y_c}^2+{(z_c-h)}^2}\\ l_b=\sqrt{{(y_c-\frac{\sqrt{3}}{2}h)}^2+{(z_c+\frac{1}{2}h)}^2}\\ l_c=\sqrt{{(y_c+\frac{\sqrt{3}}{2}h)}^2+{(z_c+\frac{1}{2}h)}^2}\end{array}\right.---\left(1\right)$

The space rope is that the robot pose kinetics equation is:

$J\stackrel{\·}{\mathrm{\ω}}=-{\mathrm{\ω}}^{\×}\mathrm{J\ω}+T_c+T_l$

Wherein, ω=[ω _xω _yω _z] ^T∈ R ³For the space rope is that robot is with respect to the component of inertial coordinates system Space Angle speed under body coordinate system; J ∈ R ^{3 * 3}For the space rope is the moment of inertia matrix of the positive definite symmetry of robot; T _c∈ R ³For the space rope is the control moment of robot self attitude coutrol mechanism, and inequality constrain is arranged: | T _c|≤| T _Cmax|; T _l∈ R ³Control moment for the tether generation.

Utilizing correction Rodrigo (MRP) parameter σ to describe the space rope is attitude under the relative target track coordinate of robot:

$\stackrel{\·}{\mathrm{\σ}}=G\left(\mathrm{\σ}\right)\mathrm{\ω}---\left(3\right)$

σ=[σ wherein ₁σ ₂σ ₃] ^T∈ R ³, matrix G (σ) is defined as follows:

$G\left(\mathrm{\σ}\right)=\frac{1}{4}[(1-{\mathrm{\σ}}^T\mathrm{\σ})I+{2\mathrm{\σ}}^{\×}+{2\mathrm{\σ\σ}}^T]---\left(4\right)$

I herein is 3 * 3 unit matrixs.

It is that robot body coordinate system transformed matrix is that the target track coordinate is tied to the space rope:

$R=I_3-\frac{4(1-{\mathrm{\σ}}^2)}{{(1+{\mathrm{\σ}}^2)}^2}\left[{\mathrm{\σ}}^{\×}\right]+\frac{8}{{(1+{\mathrm{\σ}}^2)}^2}{\left[{\mathrm{\σ}}^{\×}\right]}^2---\left(5\right)$

For the ease of subsequent analysis, utilize simple and clear Eulerian angle

(roll angle), θ (angle of pitch), ψ (crab angle) (1-2-3 rotation) come attitude is represented:

Wherein be that s () is sine function, c () is cosine function.

The space rope is that the relative position vector between robot and the platform is: s=[x _r-x _py _r-y _pz _r-z _p] ^TThe position vector between tether point and the platform then, namely the tether vector is:

l＝s-R ^-1p (7)

Tether pulling force vector is:

$F_l=\left[F_{\mathrm{lx}}{F}_{\mathrm{ly}}{F}_{\mathrm{lz}}\right]=-\frac{l}{\left|\right|\left|l\right|\left|\right|}T---\left(8\right)$

Wherein T is the tether pulling force.

The moment that pulling force produces is:

T _l＝F _l×p (9)

Can be found out by the model of setting up, when carrying out attitude controlled, need tether that pulling force is arranged, and attitude all needs to adjust in whole approximate procedure, then needs to have lasting pulling force to exist on the tether, therefore, here consider that tether adopts permanent pulling force to cook up a paths out, space rope is robot according to the path of planning to target approaches, so just can guarantee to have on the tether pulling force to exist always, controls thereby the generation control moment carries out attitude.

Approach the design of attitude controller:

Because rope is that robot needs target is carried out certain observation in the approximate procedure to target, so the control target of attitude is that the space rope is that the robot front panel aims at the mark, the line trace of going forward side by side control.Expectation attitude σ _dCan calculate through the following steps:

Restricting by the space is robot location [x _ry _rz _r] ^TCalculate the expectation attitude angle

Then by formula 6 and formula 7 simultaneous, try to achieve expectation attitude σ _dPerhaps other attitude demands according to reality provide σ _d, expectation angular velocity is ω _d(under the body series).

Attitude Tracking error σ then _eWith angular velocity error ω _eCan be expressed as:

$\left\{\begin{array}{c}{\mathrm{\σ}}_e=\mathrm{\σ}\⊗{{\mathrm{\σ}}_d}^{-1}=\frac{(1-{{\mathrm{\σ}}_d}^T{\mathrm{\σ}}_d)\mathrm{\σ}({\mathrm{\σ}}^T\mathrm{\σ}-1){\mathrm{\σ}}_d-2{\mathrm{\σ}}_d\×\mathrm{\σ}}{1+\left({\mathrm{\σ}}_d^T{\mathrm{\σ}}_d\right)\left({\mathrm{\σ}}^T\mathrm{\σ}\right)+2{\mathrm{\σ}}_d^T\mathrm{\σ}}\\ {\mathrm{\ω}}_e=\mathrm{\ω}-{\mathrm{\ω}}_d\end{array}\right.---\left(11\right)$

Then Attitude Tracking error dynamics equation is:

Jω′ _e+Jω′ _d+ω ^×Jω＝T _c (12)

The Attitude Tracking error motion is learned equation:

${\stackrel{\·}{\mathrm{\σ}}}_e=G\left({\mathrm{\σ}}_e\right){\mathrm{\ω}}_e---\left(13\right)$

The design of attitude controller is divided into two parts, first, and tether can only provide the control moment (angle of pitch and crab angle) of both direction, needs the suitable controller of design that the angle of pitch and crab angle are controlled.Second portion, roll angle be owing to can not control by tether, and therefore, considering to utilize the space rope is that the thruster of robot self is controlled separately.

Utilize sliding moding structure attitude to be carried out the design of attitude controller:

T _c＝ω ^×Jω+Jω _d′-cJG(σ _e)ω _e-λsgn(s) (14)

Sliding hyperplane s=ω wherein _e+ c σ _e, parameter c＞0;

Stability is proven.

In order to reduce shake, adopt with minor function:

$\mathrm{sgn}\left(s\right)=\left\{\begin{array}{c}1,s>\mathrm{\&epsiv;}\\ s/\mathrm{\&epsiv;},\left|s\right|<\mathrm{\&epsiv;}\\ -1,s<-\mathrm{\&epsiv;}\end{array}\right.---\left(15\right)$

Wherein ε is a little positive number.

The desired control moment that calculates is T _c, the tether pulling force under the body series is: F _Lb=F _LR, then the moment of the generation of the tether under body coordinate system is: [y _cF _Lbz-z _cF _Lbyz _cF _Lbx-dF _LbzDF _Lby-y _cF _Lbx]

y _cAnd z _cFor:

$\left\{\begin{array}{c}{z}_c=(T_{\mathrm{cy}}+{\mathrm{dF}}_{\mathrm{lbz}})/F_{\mathrm{lbx}}\\ y_c=({\mathrm{dF}}_{\mathrm{lby}}-T_{\mathrm{cz}})/F_{\mathrm{lbx}}\end{array}\right.---\left(16\right)$

Following constraint condition is satisfied in tether point position:

$\left\{\begin{array}{c}{y}_{c\min }\&le;y_c\&le;y_{c\max }\\ z_{c\min }\&le;z_c\&le;z_{c\max }\end{array}\right.---\left(17\right)$

Y wherein _Cmin, y _Cmax, z _CminAnd z _CmaxBe respectively tether point position y _cAnd z _cThe bound of moving area, by the determining positions of three tether folding and unfolding mouth a, b and the c of design.

T _CxBe that the thruster of robot self provides by space rope, satisfy constraint condition | T _Cx|≤| T _Cxmax|;

In addition, can under the condition of system stability, by the size of parameter c in the adjustment control, reduce to control required moment size as far as possible, thereby reduce T _CxFuel Consumption, simultaneously, reduce the variation moving range of tether point, namely reduce y _cAnd z _cVariation.

Claims (1)

1. The space of removable tether point rope be robot approach the attitude harmony control method, it is characterized in that step is as follows:

   Step 1: the space rope is that the rear end face of robot has three tether l _a, l _bAnd l _c, three tether l _a, l _bAnd l _cBe connected in tether point t, and tether point position must be positioned at the equilateral triangle that a, b and c consist of, the tether that is connected with platform is connected in the t point, and wherein: a, b and c are that the space restricts is that the rear end face of robot has three tether folding and unfolding mouths; Be under the robot body coordinate system at the space rope thus, a point position is [d 0 h] ^T, b point position is

   

   C point position is

   

   Tether point t is p=[d y _cz _c] ^T, y _cAnd z _cBe y direction and the z durection component of p, d be barycenter to the distance of rear end face, h be a, b or c to the distance in the rear end face center of circle, three tether length are:

   $\left\{\begin{array}{c}{l}_a=\sqrt{{y_c}^2+{(z_c-h)}^2}\\ l_b=\sqrt{{(y_c-\frac{\sqrt{3}}{2}h)}^2+{(z_c+\frac{1}{2}h)}^2}\\ l_c=\sqrt{{(y_c+\frac{\sqrt{3}}{2}h)}^2+{(z_c+\frac{1}{2}h)}^2}\end{array}\right.;$

   Step 2: design based on the attitude controller of sliding moding structure is $T_c={\mathrm{\&omega;}}^{\&times;}\mathrm{J\&omega;}+J{\stackrel{\&CenterDot;}{\mathrm{\&omega;}}}_d-\mathrm{cJG}\left({\mathrm{\&sigma;}}_e\right){\mathrm{\&omega;}}_e-\mathrm{\&lambda;sgn}\left(s\right),$ Wherein: ω be space rope be robot with respect to the component of inertial coordinates system Space Angle speed under body coordinate system, ω is by dynamics/kinematical equation $\left\{\begin{array}{c}J\stackrel{\&CenterDot;}{\mathrm{\&omega;}}={-\mathrm{\&omega;}}^{\&times;}\mathrm{J\&omega;}+T_c+T_l\\ \stackrel{\&CenterDot;}{\mathrm{\&sigma;}}=G\left(\mathrm{\&sigma;}\right)\mathrm{\&omega;}\end{array}\right.$ Obtain;

   

   With

   

   The derivative to the time of difference ω and correction rodrigue parameters σ, J are that the space rope is the moment of inertia matrix of the positive definite symmetry of robot, ω * and be the antisymmetric matrix of vector multiplication cross computing ${\mathrm{\&omega;}}^{\&times;}=\left(\begin{array}{ccc}0& {-\mathrm{\&omega;}}_3& {\mathrm{\&omega;}}_2\\ {\mathrm{\&omega;}}_3& 0& {-\mathrm{\&omega;}}_1\\ -{\mathrm{\&omega;}}_2& {\mathrm{\&omega;}}_1& 0\end{array}\right),$ ω ₁, ω ₂And ω ₃Be three components of ω, T _cFor the space rope is the control moment of robot self attitude coutrol mechanism, and inequality constrain is arranged: | T _c|≤| T _Cmax|; T _lBe the control moment that tether produces, function G (σ) is defined as follows:

   

   σ _TBe the transposition of σ, I is 3 * 3 vector of unit length, σ ^*Antisymmetric matrix for the vector multiplication cross computing ${\mathrm{\&sigma;}}^{\&times;}=\left(\begin{array}{ccc}0& {-\mathrm{\&sigma;}}_3& {\mathrm{\&sigma;}}_2\\ {\mathrm{\&sigma;}}_3& 0& {-\mathrm{\&sigma;}}_1\\ -{\mathrm{\&sigma;}}_2& {\mathrm{\&sigma;}}_1& 0\end{array}\right);$ σ _dBe expectation attitude, ω _dExpect angular velocity under the body series; Attitude Tracking error σ _eWith angular velocity error ω _eBy the error dynamics equation $\left\{\begin{array}{c}J{\stackrel{\&CenterDot;}{\mathrm{\&omega;}}}_e+J{\stackrel{\&CenterDot;}{\mathrm{\&omega;}}}_d+{\mathrm{\&omega;}}^{\&times;}\mathrm{J\&omega;}=T_c\\ {\stackrel{\&CenterDot;}{\mathrm{\&sigma;}}}_e=G\left({\mathrm{\&sigma;}}_e\right){\mathrm{\&omega;}}_e\end{array}\right.$ Obtain,

   

   With

   

   Be respectively ω _e, σ _eAnd ω _dDerivative to the time; S=ω _e+ c σ _eBe sliding hyperplane, parameter c＞0, λ＞0, sgn () is sign function;

   Step 3: control moment T _cThe y durection component and the z durection component by the realization of control tether point position, tether point in the position of rear end face is: $\left\{\begin{array}{c}{z}_c=(T_{\mathrm{cy}}+{\mathrm{dF}}_{\mathrm{lbz}})/F_{\mathrm{lbx}}\\ y_c=({\mathrm{dF}}_{\mathrm{lby}}-T_{\mathrm{cz}})/F_{\mathrm{lbx}}\end{array}\right.;$

   Wherein: T _CyAnd T _CzBe the control moment T that calculates in the step 2 _cThe y direction and the component of z direction, F _Lbx, F _LbyAnd F _LbzBeing respectively tether tensile force f l is the component of robot body coordinate x direction at the space rope;

   The equilateral triangle that tether point position is positioned at a, b and c formation, satisfy following constraint condition:

   $\left\{\begin{array}{c}{y}_{c\min }\&le;y_c\&le;y_{c\max }\\ z_{c\min }\&le;z_c\&le;z_{c\max }\end{array}\right.$

   Y wherein _Cmin, y _Cmax, z _CminAnd z _CmaxBe respectively tether point position y _cAnd z _cThe bound of moving area, by the determining positions of three tether folding and unfolding mouth a, b and the c of design;

   Control moment T _cX durection component T _CxBe that the thruster of robot self provides by space rope, satisfy constraint condition | T _Cx|≤| T _Cxmax|, T _CxmaxFor the space rope is the Maximum controlling moment of the x of robot direction;

   Step 4: provide the control moment of y direction and z direction by the adjustment of the tether point position in the step 3, the control moment of x direction is that robot self thruster provides by the space rope, has realized to the space rope being the coordination control of robot pose.

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