CN102331785B - Method for controlling spacecraft attitude directing constraint attitude maneuver - Google Patents

Abstract

The invention relates to an independent method for controlling spacecraft attitude directing constraint attitude maneuver, belonging to the technical field of spacecraft attitude control. The method comprises the following steps of: constructing a navigation function V related to the motion of the tail end point of a current pointing vector r of a sensor on a unit spherical surface S by taking the tail end point of a target pointing vector rd of the sensor as a target point position, taking the tail end point of the current pointing vector r as a current position and taking a spherical doom formed by a pointing constraint as a barrier region; designing a control torque expression according to the navigation function, and regulating the amplitude of a control torque by changing control torque parameters to drive the spacecraft to make the sensor point to the target vector rd; and driving the spacecraft to rotate in the vector direction of the sensor by an angle theta after the sensor points to the target vector rd, so that a complete attitude maneuver process of the spacecraft is realized. According to the method, pointing avoidance of the barrier region can be processed definitely, a local minimum value can be avoided for a plurality of barrier constraints simultaneously, safe maneuver of the spacecraft to a target attitude is ensured, the requirement of boundedness on an executing mechanism is met, and independent control over spacecraft directing constraint attitude maneuver is realized.

Description

A kind of method for controlling spacecraft attitude directing constraint attitude maneuver

Technical field

The invention belongs to Spacecraft Attitude Control technical field, relate to a kind of method that is subject to the autonomous attitude maneuver control of directing constraint.

Background technology

Along with the development of spacecraft technology and the variation of space mission, on spacecraft, sometimes need to install low light level Sensitive Apparatus (as infrared telescope, star sensor etc.) and complete specific detection mission.Particularly the light of the sun is very sensitive to high light celestial body for these instruments, if do not take precautions against light by necessary measure, enters in its sensitive components, is just easy to cause the damage of sensitive components.In attitude maneuver process, common way is to close these devices, but in some cases, still needs these instruments in running order, and this just requires the sensing bypassing method of invention attitude maneuver.

In processing the method for this problem, generally speaking there are two classes, the one, cook up in advance attitude maneuver sequence, then by carrying out progressively tracking sequence point, thereby complete whole attitude maneuver process; Another kind is that planning and execution are dissolved in controller simultaneously, by building energy function, barrier zone in whole work space is expressed as to high potential energy district, target place is expressed as low-potential energy district, then incorporate attitude dynamics and kinematics, draw suitable control inputs, thereby drive spacecraft attitude to rotate to targeted attitude.Last class methods generally need higher calculation cost, on star the limited spacecraft of computational resource and inadvisable.Then a class mode is less to computational resource requirement, more can better meet by contrast the requirement of real-time on star.

For rear class methods, Wisniewski, R.and P.Kulczycki is in " Slew maneuvercontrol for spacecraft equipped with star camera and reaction wheels. " literary composition, consider the situation of star sensor directing constraint, utilize Energy shaping method to complete attitude maneuver process, but do not consider the problem of actuating mechanism controls bounded, therefore can not guarantee the smooth execution of Practical Project.

Further, Radice, G.and I.Ali is in " Autonomous attitude usingpotential function method under control input saturation " literary composition, equally in the situation of considering a sensor directing constraint, consider the boundedness of topworks, obtained the control inputs of bounded.But also untreated areas directing constraint, just makes to point to axle in the process of implementation and point to away from obstacle as far as possible, be difficult to explanation and point to whether entered into the barrier zone that is oriented to center with obstacle.During in addition for a plurality of directing constraint, there is the situation of local solution in the method.

Generally speaking, existing for being subject in the attitude maneuver control method of directing constraint, the processing of evading to barrier zone problem does not also have clear and definite method, and during in addition to many Obstacles Constraints, local minimizing rejecting also considers that the method for topworks's bounded does not also occur simultaneously.

Summary of the invention

In order to evade the sensing of barrier zone clearly, local minimizing problem while simultaneously rejecting many Obstacles Constraints, in the situation that considering topworks's bounded, the present invention proposes a kind of method that spacecraft attitude directing constraint attitude maneuver is controlled, and the process of its specific implementation is as follows:

Step 1, according to the structure mount message of spacecraft itself, the sensor direction vector that obtains considering directing constraint is expressed as r under body series _b, under inertial system, be expressed as r;

According to attitude sensor information and ephemeris information, obtain spacecraft barycenter and in the expression under inertial system, be respectively r to the vector of a relevant n celestial body _oj, j=1 ..., n; According to attitude sensor information, obtain spacecraft under inertial system with respect to the attitude matrix C under body series _ib, subscript represents that this attitude matrix is the conversion from body series b to inertial system I;

According to expectation attitude matrix the target directing that obtains sensor direction vector is expressed as r under inertial system _d;

Step 2, centered by spacecraft barycenter, set up unit sphere S; According to the visual field vertex angle theta of sensor ₀and the view angle theta of a relevant n celestial body _oj, obtain sensor direction vector r and n day voxel vector r _ojbetween restriction relation be r ^tr _oj< cos θ _j, θ wherein _j=θ ₀+ θ _oj, sensor direction vector r can not enter into by j day voxel vector r in attitude maneuver process _ojfor symcenter, summit is at spacecraft barycenter, and cone apex angle is θ _jspace cone in, the sensing of n celestial body will form n space cone, these spaces bore and unit sphere S crossing after, unit sphere S is cut out to n spherical crown surface, wherein, the distance at the center of j spherical crown surface and spherical crown edge is ρ _j, ${\mathrm{\&rho;}}_j=\sqrt{2-2\mathrm{soc}{\mathrm{\&theta;}}_j};$

Step 3, on unit sphere S, with sensor target direction vector r _ddistal point be impact point position, the distal point of the direction vector r that sensor is current is current location, the formed spherical crown surface of directing constraint is barrier zone, builds the navigation function V that the distal point about r moves on sphere; Navigation function V is:

$V={\left(\frac{{\mathrm{\&gamma;}}_d^k}{{\mathrm{\&gamma;}}_d^k+\mathrm{\&beta;}}\right)}^{1/k}---\left(1\right)$

Wherein, k is constant, k>=2, γ _d=|| r-r _d|| ², β and β _jfor intermediate variable,

${\mathrm{\&beta;}}_j={\left|\right|r-r_{\mathrm{oj}}\left|\right|}^2-{\mathrm{\&rho;}}_j^2;$

Step 4, navigation function is fused in the design process of control law, in conjunction with attitude dynamics and kinematics, and utilizes progressively pusher backstepping method design control moment u expression formula, spacecraft rotation under control moment drives, control moment u is:

$u=\left[{\mathrm{\&omega;}}^{\&times;}\right]\mathrm{J\&omega;}+J({\stackrel{\&CenterDot;}{\mathrm{\&omega;}}}_s+\frac{\mathrm{\&mu;}}{\mathrm{\&eta;}}{\mathrm{\&omega;}}_s+s({\mathrm{\&omega;}}_s-\mathrm{\&omega;}))---\left(2\right)$

Wherein, μ, η, s is for regulating parameter, the inertia matrix that J is spacecraft, the attitude angular velocity that ω is spacecraft, [ω ^*] be the multiplication cross matrix of spacecraft attitude angular velocity, expectation attitude angular velocity ω _sderivative with expectation attitude angular velocity

by (3)-(7) and (8)-(14), provided respectively;

${\mathrm{\&omega;}}_s=-\frac{1}{\mathrm{\&mu;}}{(\mathrm{F\&Psi;}-\mathrm{G\&Xi;})}^T---\left(3\right)$

Wherein, F, Ψ, G, Ξ are intermediate variable, and expression is as follows:

$F={({\mathrm{\&gamma;}}_d^k+\mathrm{\&beta;})}^{-1/k}-{({\mathrm{\&gamma;}}_d^k+\mathrm{\&beta;})}^{-1-1/k}{\mathrm{\&gamma;}}_d^k---\left(4\right)$

$G={\mathrm{\&gamma;}}_d\frac{{({\mathrm{\&gamma;}}_d^k+\mathrm{\&beta;})}^{-1/k-1}}{k}---\left(5\right)$

Ψ＝-2(r-r _d) ^T(C _Ib[r _b×]) （6）

Wherein, r _b=[r _b1, r _b2, r _b3] ^t, [r _b*] be multiplication cross matrix, its form is $\left[\begin{array}{ccc}0& {-r}_{b3}& r_{b2}\\ r_{b2}& 0& -r_{b1}\\ -r_{b2}& r_{b1}& 0\end{array}\right],$

$\mathrm{\&Xi;}=\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}\left(\left(\underset{i=1}{\underset{i\&NotEqual;j}{\overset{n}{\mathrm{\&Pi;}}}}{\mathrm{\&beta;}}_i\right)(-2{(r-r_{\mathrm{oj}})}^T\left(C_{\mathrm{Ib}}\right[r_b\&times;\left]\right))\right)---\left(7\right)$

${\stackrel{\&CenterDot;}{\mathrm{\&omega;}}}_s=-\frac{1}{\mathrm{\&mu;}}(\stackrel{\&CenterDot;}{F}\mathrm{\&Psi;}+F\stackrel{\&CenterDot;}{\mathrm{\&Psi;}}-\stackrel{\&CenterDot;}{G}\mathrm{\&Xi;}-G\stackrel{\&CenterDot;}{\mathrm{\&Xi;}})---\left(8\right)$

Wherein,

be intermediate variable, expression is as follows:

$\stackrel{\&CenterDot;}{F}=((-1/k){({\mathrm{\&gamma;}}_d^k+\mathrm{\&beta;})}^{-1/k-1}({\mathrm{k\&gamma;}}_d^{k-1}\mathrm{\&Psi;}+\mathrm{\&Xi;})+---\left(9\right)$

$(1+1/k){({\mathrm{\&gamma;}}_d^k+\mathrm{\&beta;})}^{-2-1/k}{r}_d^k({\mathrm{k\&gamma;}}_d^{k-1}\mathrm{\&Psi;}+\mathrm{\&Xi;})-{({\mathrm{\&gamma;}}_d^k+\mathrm{\&beta;})}^{-1-1/k}{\mathrm{k\&gamma;}}_d^{k-1}\mathrm{\&Psi;})\mathrm{\&omega;}$

$\stackrel{\&CenterDot;}{\mathrm{\&Psi;}}=-2{\left({-C}_{\mathrm{Ib}}\right[r_b\&times;\left]\mathrm{\&omega;}\right)}^T\left(C_{\mathrm{Ib}}\right[r_b\&times;\left]\right)-2{(r-r_b)}^T\left(C_{\mathrm{Ib}}\right[\mathrm{\&omega;}\&times;\left]\right[r_b\&times;\left]\right)---\left(10\right)$

$\stackrel{\&CenterDot;}{G}=(\frac{{({\mathrm{\&gamma;}}_d^k+\mathrm{\&beta;})}^{-1/k-1}}{k}\mathrm{\&Psi;}+{\mathrm{\&gamma;}}_d\frac{(-1/k-1){({\mathrm{\&gamma;}}_d^k+\mathrm{\&beta;})}^{-1/k-2}({\mathrm{k\&gamma;}}_d^{k-1}\mathrm{\&Psi;}+\mathrm{\&Xi;})}{k})\mathrm{\&omega;}---\left(11\right)$

$\stackrel{\&CenterDot;}{\mathrm{\&Xi;}}=\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}(\underset{l\&NotEqual;j}{\underset{l=1}{\overset{n}{\mathrm{\&Sigma;}}}}\left({\stackrel{\&CenterDot;}{\mathrm{\&beta;}}}_l\underset{i=l}{\underset{i\&NotEqual;l}{\underset{i\&NotEqual;j}{\overset{n}{\mathrm{\&Pi;}}}}}{\mathrm{\&beta;}}_i\right)B_j+\left(\underset{i=1}{\underset{i\&NotEqual;j}{\overset{n}{\mathrm{\&Pi;}}}}{\mathrm{\&beta;}}_i\right){\stackrel{\&CenterDot;}{B}}_j)---\left(12\right)$

Wherein, B _j,

be intermediate variable, expression is as follows:

B _j＝-2(r-r _oj) ^TC _Ib[r _b×] （13）

${\stackrel{\&CenterDot;}{B}}_j=-2{\stackrel{\&CenterDot;}{r}}^T\left(C_{\mathrm{Ib}}\right[r_b\&times;\left]\right)-2{(r-r_{\mathrm{oj}})}^T\left(C_{\mathrm{Ib}}\right[\mathrm{\&omega;}\&times;\left]\right[r_b\&times;\left]\right)---\left(14\right)$

Due to navigation function can guarantee sensor except navigation function limited several saddle points, all will be motor-driven to dbjective state from original state safely, thereby can avoid the appearance of local minimum.

Step 5, according to control moment expression formula definite in step 4, by change, control parameter μ, η and s, adjust the amplitude of control moment, thereby meet the output requirement of spacecraft topworks;

$\left|\right|u\left|\right|\&le;\left|\right|J\left|\right|({\tilde{D}}^2+(\tilde{P}+\tilde{Q}+\frac{\mathrm{\&mu;}}{\mathrm{\&eta;}})\tilde{D}+{\left|\right|e\left|\right|}^2+(\tilde{P}+\tilde{Q}+2\tilde{D}+1)|\left|e\right|\left|\right)---\left(15\right)$

Wherein,

be normal value,

|| e|| is intermediate variable, and expression is as follows:

$\tilde{P}=\left(\begin{array}{c}4\left({(4^k+4^n)}^{-1/k-1}(\frac{1}{k}(k{4}^k+n{4}^n)+(1+\frac{1}{k})\frac{4^k(k{4}^k+n{4}^n)}{4^k+4^n}+k{4}^k)\right)\\ +2({(4^k+4^n)}^{-1/k}+4^k{(4^k+4^n)}^{-1-1/k})+\\ n{4}^n\frac{1}{k}{(4^k+4^n)}^{-1/k-1}(4+(\frac{1}{k}+1)\frac{k{4}^k+n{4}^n}{4^k+4^n})\\ +4^{n+1}(\frac{1}{2}+\frac{3n}{2}+n^2)\left(\frac{4{(4^k+4^n)}^{-1/k-1}}{k}\right)\end{array}\right)---\left(16\right)$

$\tilde{Q}=(4({(4^k+4^n)}^{-1/k}+4^k{(4^k+4^n)}^{-1-1/k})+4^n(\frac{1}{2}+n(n-1))\left(\frac{4{(4^k+4^n)}^{-1/k-1}}{k}\right))---\left(17\right)$

$\tilde{D}=\frac{4{(4^k+4^n)}^{-1/k}}{\mathrm{\&mu;}}(1+\frac{4^k}{4^k+4^n}+\frac{{n4}^n}{k(4^k+4^n)})---\left(18\right)$

$\left|\right|e\left|\right|\&le;\max \{\frac{\mathrm{\&mu;}\tilde{D}}{s},e\left(t_0\right)\}---\left(19\right)$

From formula (16) and (17)

be constant, formula (18) and (19) are visible

|| e|| is along with parameter μ, and therefore the variation of η and s and changing, controls parameter μ by adjustment, η and s, and then regulate

with || the size of e||, can adjust the boundary of control inputs;

Step 6, according to step 4 and the determined control moment of step 5, drive spacecraft, thereby make sensor point to target vector r _d;

Step 7, spacecraft complete sensor and point to target vector r _dafter, need again around sensor direction vector anglec of rotation θ, thereby realize the attitude maneuver process that spacecraft is complete; Wherein, definite formula of angle θ is as follows:

$\mathrm{\&theta;}=2\mathrm{ar}\cos \left(Q_{e_0}\right)---\left(20\right)$

Wherein,

for deviation attitude quaternion Q _emark portion, Q _eby deviation attitude matrix

it is converted,

for spacecraft attitude matrix,

for final targeted attitude matrix.

Beneficial effect

(1) the inventive method, the navigation function moving on sphere by the distal point building about r, can evade and processing the sensing of barrier zone clearly, rather than as prior art, just makes to point to axle as far as possible and point to away from obstacle.

(2) during simultaneously for a plurality of Obstacles Constraints, can avoid local minimum, guarantee that spacecraft safety is motor-driven to targeted attitude.

(3) by the adjustment of control moment and determining of control inputs border, meet the requirement of topworks's boundedness, realized the control of autonomous spacecraft attitude directing constraint attitude maneuver.

Accompanying drawing explanation

Fig. 1 is the directing constraint attitude figure of embodiment of the present invention;

Fig. 2 is posture restraint mapping graph;

Fig. 3 is the motion path of sensor direction vector end in unit sphere in concrete case study on implementation;

Fig. 4 is the time history of control moment input in concrete case study on implementation.

Embodiment

Below in conjunction with accompanying drawing, the embodiment of the inventive method is elaborated.

A method for controlling spacecraft attitude directing constraint attitude maneuver, its concrete steps comprise:

Step 1, as shown in Figure 1, establishes and need to consider that the infrared senstive device of directing constraint points to the r that is expressed as under body series _b=[0.12,0.24,0.963] ^t; Spacecraft barycenter is the component r under inertial system to the direction vector of the sun _o1=[1,0,0] ^t, spacecraft barycenter is the component r under inertial system to the direction vector of Saturn _o2=[0.5 ,-0.866,0] ^t, spacecraft barycenter is the component r under inertial system to the direction vector of Jupiter _o3=[0.5,0.866,0] ^t; Can according to attitude sensor information, obtain inertial system with respect to the attitude matrix C of spacecraft body series in real time _ib.Initial time spacecraft attitude matrix is $C_{\mathrm{Ib}}=\left[\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ 0& 0& 1\end{array}\right],$ Angular velocity under body series is ω=[0,0,0] ^t.The component of sensor direction vector under inertial system is r(r=C _ibr _b).Expression r according to sensor under body series _band expectation attitude matrix $C_{\mathrm{Ib}}^d=\left[\begin{array}{ccc}0.4602& -0.6354& 0.6201\\ -0.8786& -0.4261& 0.2156\\ 0.1272& -0.6440& -0.7543\end{array}\right],$ The target directing that obtains sensor direction vector is expressed as r under inertial system _d=[0.5,0 ,-0.866].

Step 2, the visual field vertex angle theta of establishing sensor ₀the visual angle of=14 ° and relevant celestial body is respectively θ _o1=3 °, θ _o2=1 °, θ _o3=2 °, θ ₁=θ ₀+ θ _d=17 °, θ ₂=θ ₀+ θ _o2=15 °, θ ₃=θ ₀+ θ _o3=16 °.As shown in Figure 2, the center of 1st spherical crown surface relevant to the sun and the distance at spherical crown edge are

the center of 2nd spherical crown surface and the distance at spherical crown edge relevant to Saturn are

the center of 3rd spherical crown surface and the distance at spherical crown edge relevant to Jupiter are

Step 3, according to navigation functional form, by the r obtaining in step 1 and step 2 _dbe brought into γ _din, by r _oj(j=1,2,3) and ρ _j(j=1,2,3) are brought into β _jin (j=1,2,3).In addition, k=2, N=3.

Step 4, utilize progressively the controlled moment input of pusher backstepping method expression formula

$u=\left[{\mathrm{\&omega;}}^{\&times;}\right]\mathrm{J\&omega;}+J({\stackrel{\&CenterDot;}{\mathrm{\&omega;}}}_s+\frac{\mathrm{\&mu;}}{\mathrm{\&eta;}}{\mathrm{\&omega;}}_s+s({\mathrm{\&omega;}}_s-\mathrm{\&omega;}))$

Wherein, the inertia matrix of spacecraft $J=\left[\begin{array}{ccc}100& & \\ & 100& \\ & & 100\end{array}\right]\mathrm{kg}\&CenterDot;m^2.$ ω is that spacecraft is being controlled the component of angular velocity constantly under body series, ω _sfor controlling expectation angular velocity constantly,

for controlling the derivative of expecting angular velocity constantly.μ, η and s are adjusting parameter, and are all arithmetic number.

Step 5, for control inputs, express formula, design parameter μ=12, η=30, s=0.5, makes the peak value of control moment be less than 1Nm.

Step 6, according to step 4 and the determined control moment of step 5, drive spacecraft, thereby make sensor point to target vector r _d.

Step 7, at γ _damplitude reach 10 ^-9after, control is switched to the large angle maneuver around sensor direction vector. $C_{\mathrm{Ib}}^s=\left[\begin{array}{ccc}-0.0632& -0.7080& 0.7034\\ -0.9825& 0.1678& 0.0806\\ -0.1751& -0.6860& -0.7062\end{array}\right]$ For the attitude matrix of spacecraft at switching instant, according to targeted attitude matrix $C_{\mathrm{Ib}}^d=\left[\begin{array}{ccc}0.4602& -0.6354& 0.6201\\ -0.8786& -0.4261& 0.2156\\ 0.1272& -0.6640& -0.7543\end{array}\right],$ Can try to achieve deviation attitude matrix is $C_{\mathrm{Ib}}^e=C_{\mathrm{Ib}}^d{\left(C_{\mathrm{Ib}}^s\right)}^T=\left[\begin{array}{ccc}0.8569& -0.5088& -0.0827\\ 0.5088& 0.8092& 0.2939\\ -0.0827& -0.2939& 0.9523\end{array}\right],$ And then try to achieve deviation hypercomplex number and be ${\mathrm{<figure-callout\; id="0"\; label="Q\; e"\; filenames="HDA0000076247450000011.png,HDA0000076247450000013.png"\; state="\{\{state\}\}">Q</figure-callout>}}_{e_{}}={[\mathrm{0.9511,0.1545,0},-0.2675]}^T,$ Finally obtain around the sensor direction vector anglec of rotation

By method above, set forth, the method is simulated specifically as shown in Figure 3.By Spherical Surface S ²by longitude and latitude, be launched into plane, according to potential energy curves such as navigation function draftings, and the end orbit of sensor direction vector be plotted in this plane.As seen from Figure 3, the spherical crown surface barrier zone being formed by three celestial bodies is walked around in the path of the distal point of sensor direction vector on sphere safely, and reaches target directing distal point.The time history Drawing of Curve of three components of control moment u, in Fig. 4, can be seen to three component u _x, u _y, u _zmaximum amplitude be all no more than the 1Nm of expectation.

Although combine accompanying drawing, described embodiments of the present invention, to those skilled in the art, under the premise without departing from the principles of the invention, can also make some improvement, these also should be considered as belonging to protection scope of the present invention.

Claims (1)

1. the method that spacecraft attitude directing constraint attitude maneuver is controlled, is characterized in that: the detailed process that the method realizes is as follows:

Step 1, according to the structure mount message of spacecraft itself, the sensor direction vector that obtains directing constraint is expressed as r under body series _b, under inertial system, be expressed as r;

According to attitude sensor information and ephemeris information, obtain spacecraft barycenter and in the expression under inertial system, be respectively r to the vector of a relevant n celestial body _oj, j=1 ..., n; According to attitude sensor information, obtain spacecraft under inertial system with respect to the attitude matrix C under body series _ib, subscript represents that this attitude matrix is the conversion from body series b to inertial system I;

According to expectation attitude matrix obtain sensor under inertial system and point to target vector r _d;

Step 2, centered by spacecraft barycenter, set up unit sphere S; According to the visual field vertex angle theta of sensor ₀and the view angle theta of a relevant n celestial body _oj, obtain sensor direction vector r and n day voxel vector r _ojbetween restriction relation be r ^tr _oj< cos θ _j, θ wherein _j=θ ₀+ θ _oj, sensor direction vector r can not enter into by j day voxel vector r in attitude maneuver process _ojfor symcenter, summit is at spacecraft barycenter, and cone apex angle is θ _jspace cone in, the sensing of n celestial body will form n space cone, these spaces bore and unit sphere S crossing after, unit sphere S is cut out to n spherical crown surface, wherein, the distance at the center of j spherical crown surface and spherical crown edge is ρ _j, ${\mathrm{\&rho;}}_j=\sqrt{2-2\cos {\mathrm{\&theta;}}_j};$

Step 3, on unit sphere S, with sensor, point to target vector r _ddistal point be impact point position, the distal point of the direction vector r that sensor is current is current location, the formed spherical crown surface of directing constraint is barrier zone, builds the navigation function V that the distal point about r moves on sphere; Navigation function V is:

${V=\left(\frac{{\mathrm{\&gamma;}}_d^k}{{\mathrm{\&gamma;}}_d^k+\mathrm{\&beta;}}\right)}^{1/k}---\left(1\right)$

Wherein, k is constant, k>=2, γ _d=|| r-r _d|| ², β and β _jfor intermediate variable,

${\mathrm{\&beta;}}_j={\left|\right|r-r_{\mathrm{oj}}\left|\right|}^2-{\mathrm{\&rho;}}_j^2;$

Step 4, navigation function is fused in the design process of control law, in conjunction with attitude dynamics and kinematics, and utilizes method of inversion backstepping design control moment u expression formula, spacecraft rotation under control moment drives; Control moment u is:

$u=\left[{\mathrm{\&omega;}}^{\&times;}\right]\mathrm{J\&omega;}+J({\stackrel{\&CenterDot;}{\mathrm{\&omega;}}}_s+\frac{\mathrm{\&mu;}}{\mathrm{\&eta;}}{\mathrm{\&omega;}}_s+s({\mathrm{\&omega;}}_s-\mathrm{\&omega;}))---\left(2\right)$

Wherein, μ, η, s is for regulating parameter, the inertia matrix that J is spacecraft, the attitude angular velocity that ω is spacecraft, ω _sfor expectation attitude angular velocity and

for the derivative of expectation attitude angular velocity, [ω ^*] be the multiplication cross matrix of spacecraft attitude angular velocity;

Step 5, according to control moment expression formula definite in step 4, by change, control parameter μ, η and s, adjust the amplitude of control moment, thereby meet the output requirement of spacecraft topworks;

Step 6, according to step 4 and the determined control moment of step 5, drive spacecraft, thereby make sensor point to target vector r _d;

Step 7, spacecraft complete sensor and point to target vector r _dafter do not reach complete targeted attitude, need around sensor direction vector, to rotate to an angle again, thereby realize the attitude maneuver process that spacecraft is complete.

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