CN105912005A

CN105912005A - Space non-cooperative target attitude joint takeover control method utilizing tether thruster

Info

Publication number: CN105912005A
Application number: CN201610323425.5A
Authority: CN
Inventors: 孟中杰; 张志斌; 黄攀峰; 王秉亨; 常海涛; 刘正雄
Original assignee: Northwestern Polytechnical University
Current assignee: Northwestern Polytechnical University
Priority date: 2016-05-16
Filing date: 2016-05-16
Publication date: 2016-08-31
Anticipated expiration: 2036-05-16
Also published as: CN105912005B

Abstract

The invention discloses a space non-cooperative target posture joint takeover control method using a tether thruster. Firstly, the control command and the state measurement value are generated through the formula to generate an error command, and then some parameters of the controller are updated online in real time, and then the attitude is used to automatically The adaptive control law generates a pseudo-control quantity: the control torque. Then transform the distribution problem of the control quantity into a robust optimization problem, transform the robust optimization problem into a cone quadratic optimization problem, and use the interior point method to solve it to obtain the real control quantity: thrust and tension, and finally drive 12 thrusts respectively and tether tension to achieve joint attitude takeover control of non-cooperative targets.

Description

Attitude joint takeover control method for non-cooperative targets in space using tether thrusters

【技术领域】【Technical field】

本发明属于航天器姿态控制领域，涉及一种利用系绳推力器的空间非合作目标姿态联合接管控制方法。The invention belongs to the field of attitude control of spacecraft, and relates to a joint takeover control method of a space non-cooperative target attitude by using a tether thruster.

【背景技术】【Background technique】

接管控制是指利用服务航天器的操作机构与目标航天器形成固定连接后，利用姿轨控制系统接管目标航天器的姿轨控制系统，实现其姿轨控制。随着空间技术的发展，在轨服务受到了越来越多的重视。针对在废弃轨道搁浅的卫星、姿态翻滚造成失效的卫星、姿态指向错误造成无法正常工作的卫星等，如果能利用服务航天器对其进行姿态接管，为其提供辅助变轨、辅助定姿等接管控制，将具有极大的经济效益和社会影响。德国DLR的DEOS(Deutsche Orbital Servicing)项目，欧空局的SMART-OLEV(SMART Orbital LifeExtension Vehicle)项目，美国的FREND(Front-end Robotics Enabling Near-termDemonstration)项目等均针对此类问题进行研究和准备开展在轨试验。Takeover control refers to the use of the attitude-orbit control system to take over the attitude-orbit control system of the target spacecraft after the operating mechanism of the serving spacecraft forms a fixed connection with the target spacecraft to realize its attitude-orbit control. With the development of space technology, on-orbit service has received more and more attention. For satellites that are stranded in abandoned orbits, satellites that fail due to attitude rollover, and satellites that cannot work normally due to incorrect attitude pointing, if the service spacecraft can be used to take over their attitude, provide them with auxiliary orbit change, auxiliary attitude determination, etc. Control will have great economic benefits and social impact. The DEOS (Deutsche Orbital Servicing) project of DLR in Germany, the SMART-OLEV (SMART Orbital Life Extension Vehicle) project of ESA, and the FREND (Front-end Robotics Enabling Near-term Demonstration) project of the United States are all researching and preparing for such problems Conduct on-orbit tests.

但是，目前研究的接管控制多是利用服务航天器携带机械臂等刚性空间机器人抓捕目标，然后利用服务航天器的姿轨控制系统接管控制目标航天器。空间绳系机器人是一种新型的刚柔组合空间机器人系统，具有操作距离远、安全、灵活等优势，近年来得到了广泛关注。由于需要远距离逼近目标航天器，空间绳系机器人的操作机构具有推力器。因此，可利用推力器和系绳对目标航天器进行联合接管控制。王东科等人进行了系绳与推力器联合进行目标姿态控制的研究。但是，其将目标惯量视为已知，且未考虑控制量分配、控制量受约束等问题，而认为空间绳系机器人的操作机构可利用推力器输出任何控制力矩。实际上，针对非合作目标，目标星的转动惯量未知，推力器输出力矩受限，且目标星质心位置未知也导致了推力作用点、作用方向均未知。这些问题极大的增加了利用系绳/推力器联合进行目标星姿态接管控制的难度。针对此难题，本发明充分考虑这些未知和受限状态量及控制量，给出一种非合作目标星的姿态接管控制方法。However, most of the takeover control currently studied is to use the service spacecraft to carry rigid space robots such as manipulators to capture the target, and then use the attitude and orbit control system of the service spacecraft to take over and control the target spacecraft. Space tethered robot is a new type of rigid-flexible combined space robot system, which has the advantages of long operating distance, safety, and flexibility, and has received extensive attention in recent years. Due to the need to approach the target spacecraft at a long distance, the operating mechanism of the space tethered robot has a thruster. Therefore, joint takeover control of the target spacecraft can be performed using thrusters and tethers. Wang Dongke and others carried out the research on target attitude control by tether and thruster. However, it regards the target inertia as known, and does not consider the distribution of control quantities, the constraints of control quantities, etc., and believes that the operating mechanism of the space tethered robot can use the thruster to output any control torque. In fact, for non-cooperative targets, the moment of inertia of the target star is unknown, the output torque of the thruster is limited, and the position of the center of mass of the target star is unknown, which leads to unknown thrust point and direction. These problems greatly increase the difficulty of using the tether/thruster combination to take over the target star attitude control. Aiming at this problem, the present invention fully considers these unknown and limited state quantities and control quantities, and provides an attitude takeover control method for non-cooperative target stars.

【发明内容】【Content of invention】

本发明的目的在于解决空间非合作目标星的姿态接管控制问题，提供一种利用系绳推力器的空间非合作目标姿态联合接管控制方法。The object of the present invention is to solve the problem of attitude takeover control of space non-cooperative target stars, and provide a space non-cooperative target attitude joint takeover control method using tether thrusters.

为达到上述目的，本发明采用以下技术方案予以实现：In order to achieve the above object, the present invention adopts the following technical solutions to achieve:

利用系绳推力器的空间非合作目标姿态联合接管控制方法，包括以下步骤：A joint takeover control method for a space non-cooperative target attitude using a tether thruster, comprising the following steps:

1)建立空间非合作目标星姿态接管控制模型；1) Establish a space non-cooperative target star attitude takeover control model;

2)设计非合作目标星的姿态自适应接管控制律；2) Design the attitude adaptive takeover control law of the non-cooperative target star;

3)接管控制力矩的鲁棒分配。3) Take over the robust distribution of control moments.

本发明进一步的改进在于：The further improvement of the present invention is:

所述步骤1)中，建立空间非合作目标星姿态接管控制模型的具体方法为：In the described step 1), the specific method of setting up the space non-cooperative target star attitude takeover control model is:

以O_T为空间非合作目标星的质心，建立目标星本体系O_TX_TY_TZ_T，以O_G为操作机构的质心，建立操作机构本体系O_GX_GY_GZ_G，O_C为系绳与操作机构的连接点；为简化建模过程，假设两个坐标系各坐标轴均相互平行，设操作机构质心O_G在目标星本体系O_TX_TY_TZ_T下的坐标为X_G＝[x_G,y_G,z_G]；Take O _T as the center of mass of the non-cooperative target star in space, establish the target star system O _T X _T Y _T Z _T , take O _G as the center of mass of the operating mechanism, establish the operating mechanism system O _G X _G Y _G Z _G , O _C is the connection point between the tether and the operating mechanism; in order to simplify the modeling process, it is assumed that the coordinate axes of the two coordinate systems are parallel to each other, and the center of mass O _G of the operating mechanism is located at the target star system O _T X _T Y _T Z _T The coordinates are X _G =[x _G , y _G , z _G ];

四组操作机构，共12个推力器呈“十”字安装；其中，第1组操作机构(4)与第2组操作机构(5)包含5个正交安装的推力器，第3组操作机构(6)与第4组操作机构(7)各为1个推力器；Four sets of operating mechanisms, a total of 12 thrusters are installed in the shape of a "ten"; among them, the first set of operating mechanisms (4) and the second set of operating mechanisms (5) include 5 orthogonally installed thrusters, and the third set of operating The mechanism (6) and the fourth group of operating mechanism (7) are each a thruster;

设每个推力器的推力范围为[0 a]N，则12个推力器在操作机构本体系产生的推力及在操作机构本体系的作用点位置为：Assuming that the thrust range of each thruster is [0 a]N, the thrust generated by the 12 thrusters in the system of the operating mechanism and the position of the action point in the system of the operating mechanism are:

第一组：First group:

第二组：Second Group:

第三组及第四组：The third and fourth groups:

为简化建模过程，假设其方向不变且沿操作机构本体系-x方向；因此，设系绳最大拉力为a₅N，系绳拉力及作用点在操作机构本体系下表示为：In order to simplify the modeling process, it is assumed that its direction remains unchanged and is along the -x direction of the operating mechanism itself; therefore, the maximum tension of the tether is a ₅ N, and the tension and action point of the tether are expressed in the operating mechanism itself as:

张力tension 作用点Action point 张力约束tension constraint 系绳tether F₁₃＝[-F_13x,0,0]F ₁₃ =[-F _13x ,0,0] X₅＝[x₅,y₅,z₅]X ₅ =[x ₅ ,y ₅ ,z ₅ ] 0N≤F_13x≤a₅N0N≤F _13x ≤a ₅ N

由于操作对象为非合作目标，测量装置和执行机构均安装于空间绳系机器人的操作机构上，因此，在操作机构本体系下，建立空间非合作目标性的姿态动力学方程为：Since the operating object is a non-cooperative target, the measurement device and the actuator are installed on the operating mechanism of the space tethered robot. Therefore, under the system of the operating mechanism, the attitude dynamic equation of the non-cooperative target in space is established as:

$J J \overset{\cdot &Center Dot;}{ω ω} + + {ω ω}^{\times \times} J J ω ω = = T T + + {T T}_{d d} - - - - - - ((11))$

其中，J为目标星转动惯量矩阵，ω为目标星的角速度，^×为叉乘算子，T_d为干扰力矩，T＝T_c+T_t为控制力矩，T_c为推力器产生的控制力矩：Among them, J is the moment of inertia matrix of the target star, ω is the angular velocity of the target star, ^× is the cross product operator, T _d is the disturbance torque, T=T _c +T _t is the control torque, T _c is the control torque generated by the thruster :

${T T}_{c c} = = {Σ Σ}_{i i = = 11}^{55} (({X x}_{G G} + + {X x}_{11})) \times \times {F f}_{i i} + + {Σ Σ}_{i i = = 66}^{1010} (({X x}_{G G} + + {X x}_{22})) \times \times {F f}_{i i} + + (({X x}_{G G} + + {X x}_{33})) \times \times {F f}_{1111} + + (({X x}_{G G} + + {X x}_{44})) \times \times {F f}_{1212} - - - - - - ((22))$

F_i为第i个推力器对应的推力，i为推力器的标号，T_t为系绳产生的控制力矩：F _i is the thrust corresponding to the ith thruster, i is the label of the thruster, and T _t is the control torque generated by the tether:

T_t＝(X_G+X₅)×F₁₃ (3)T _t =(X _G +X ₅ )×F ₁₃ (3)

则控制力矩T化简为：Then the control torque T is simplified as:

$T T = = {T T}_{c c} + + {T T}_{t t} = = D D. F f = = {[\begin{matrix} 00 & (({z z}_{G G} + + {z z}_{11})) & - - (({y the y}_{G G} + + {y the y}_{11})) \\ 00 & - - (({z z}_{G G} + + {z z}_{11})) & (({y the y}_{G G} + + {y the y}_{11})) \\ (({z z}_{G G} + + {z z}_{11})) & 00 & - - (({x x}_{G G} + + {x x}_{11})) \\ (({y the y}_{G G} + + {y the y}_{11})) & - - (({x x}_{G G} + + {x x}_{11})) & 00 \\ - - (({y the y}_{G G} + + {y the y}_{11})) & (({x x}_{G G} + + {x x}_{11})) & 00 \\ 00 & (({z z}_{G G} + + {z z}_{22})) & - - (({y the y}_{G G} + + {y the y}_{22})) \\ 00 & - - (({z z}_{G G} + + {z z}_{22})) & (({y the y}_{G G} + + {y the y}_{22})) \\ - - (({z z}_{G G} + + {z z}_{22})) & 00 & (({x x}_{G G} + + {x x}_{22})) \\ (({y the y}_{G G} + + {y the y}_{22})) & - - (({x x}_{G G} + + {x x}_{22})) & 00 \\ - - (({y the y}_{G G} + + {y the y}_{22})) & (({x x}_{G G} + + {x x}_{22})) & 00 \\ - - (({y the y}_{G G} + + {y the y}_{33})) & (({x x}_{G G} + + {x x}_{33})) & 00 \\ (({y the y}_{G G} + + {y the y}_{33})) & - - (({x x}_{G G} + + {x x}_{33})) & 00 \\ 00 & - - (({z z}_{G G} + + {z z}_{55})) & (({y the y}_{G G} + + {y the y}_{55})) \end{matrix}]}^{T T} [\begin{matrix} {F f}_{11 x x} \\ {F f}_{22 x x} \\ {F f}_{33 y the y} \\ {F f}_{44 z z} \\ {F f}_{55 z z} \\ {F f}_{66 x x} \\ {F f}_{77 x x} \\ {F f}_{88 y the y} \\ {F f}_{99 z z} \\ {F f}_{1010 z z} \\ {F f}_{1111 z z} \\ {F f}_{1212 z z} \\ {F f}_{1313 x x} \end{matrix}] - - - - - - ((44))$

其中，D为控制量分配矩阵，F为执行器组成的列向量；Among them, D is the control quantity allocation matrix, and F is the column vector composed of actuators;

利用修正罗德里格斯参数描述的目标星姿态运动学方程为：The attitude kinematic equation of the target star described by the modified Rodriguez parameters is:

$\overset{\cdot \cdot}{σ σ} = = G G ((σ σ)) ω ω - - - - - - ((55))$

$G G ((σ σ)) = = \frac{11}{44} [[((11 - - {σ σ}^{T T} σ σ)) {I I}_{33} + + 22 {σ σ}^{\times \times} + + 22 {σσ σσ}^{T T}]] - - - - - - ((66))$

其中，σ为目标星的姿态修正罗德里格斯参数，I₃为3×3的单位矩阵；Among them, σ is the attitude correction Rodrigues parameter of the target star, and I ₃ is a 3×3 identity matrix;

设非合作目标星的期望姿态为σ_d，期望角速度为ω_d，则目标星姿态误差动力学/运动学方程为：Suppose the expected attitude of the non-cooperative target star is σ _d , and the expected angular velocity is ω _d , then the dynamics/kinematics equation of the attitude error of the target star is:

$\{\begin{matrix} {\overset{\cdot \cdot}{σ σ}}_{e e} = = G G (({σ σ}_{e e})) {ω ω}_{e e} \\ J J {\overset{\cdot &Center Dot;}{ω ω}}_{e e} = = - - {((ω ω))}^{\times \times} J J ((ω ω)) - - {Jω Jω}_{d d} + + T T + + {T T}_{d d} \end{matrix} - - - - - - ((77))$

其中，σ_e为姿态误差，ω_e为角速度误差，两者的表达式为：Among them, σ _e is the attitude error, ω _e is the angular velocity error, and the expressions of the two are:

$\{\begin{matrix} {σ σ}_{e e} = = σ σ &CircleTimes; &CircleTimes; {σ σ}_{d d}^{- - 11} = = \frac{((11 - - {σ σ}_{d d}^{T T} {σ σ}_{d d})) σ σ + + (({σ σ}^{T T} σ σ - - 11)) {σ σ}_{d d} - - 22 {σ σ}_{d d} \times \times σ σ}{11 + + (({σ σ}_{d d}^{T T} {σ σ}_{d d})) (({σ σ}^{T T} σ σ)) + + 22 {σ σ}_{d d}^{T T} σ σ} \\ {ω ω}_{e e} = = ω ω - - {ω ω}_{d d} \end{matrix} - - - - - - ((88))$

式(8)中，表示MRP乘法。In formula (8), Indicates MRP multiplication.

所述步骤2)中，设计非合作目标星的姿态自适应接管控制律的方法为：Described step 2) in, the method for the attitude adaptive takeover control law of design non-cooperative target star is:

首先，定义辅助误差变量：s＝ω_e+ασ_e，α≥0，则First, define the auxiliary error variable: s=ω _e +ασ _e , α≥0, then

$\begin{matrix} J J \overset{\cdot \cdot}{s the s} = = J J {\overset{\cdot &Center Dot;}{ω ω}}_{e e} + + J J α α {\overset{\cdot \cdot}{σ σ}}_{e e} \\ = = - - {((ω ω))}^{\times \times} J J ((ω ω)) - - {Jω Jω}_{d d} + + T T + + {T T}_{d d} + + α α J J G G (({σ σ}_{e e})) {ω ω}_{e e} \\ = = T T + + L L \end{matrix} - - - - - - ((99))$

其中，L＝-(ω)×J(ω)-[J+αJG(σ_e)]ω_d+T_d+αJG(σ_e)ω；用||·||表示矢量的欧几里得范数，对||L||进行分析：Among them, L=-(ω)×J(ω)-[J+αJG(σ _e )]ω _d +T _d +αJG(σ _e )ω; use |||| Number, analyze ||L||:

由于ω_d有界；设外部扰动T_d的欧几里得范数满足||T_d||≤c_d0+c_d1||ω||²，c_d0和c_d1均为未知且非负的常数，则：because ω _d is bounded; suppose the Euclidean norm of external disturbance T _d satisfies ||T _d ||≤c _d0 +c _d1 ||ω|| ² , c _d0 and c _d1 are both unknown and non-negative constants ,but:

||L||≤b₀+b₁||ω||+b₂||ω||² (10)||L||≤b ₀ +b ₁ ||ω||+b ₂ ||ω|| ² (10)

其中，b₀、b₁和b₂均为未知且非负的常数；Among them, b ₀ , b ₁ and b ₂ are all unknown and non-negative constants;

然后，在此基础上，设计姿态自适应控制律：Then, on this basis, the attitude adaptive control law is designed:

$T T = = - - {k k}_{11} {ασ ασ}_{e e} - - {k k}_{22} \frac{sgn sgn ((s the s))}{| | | | s the s | | | |} - - (({\overset{^^}{b b}}_{00} + + {\overset{^^}{b b}}_{11} | | | | ω ω | | | | + + {\overset{^^}{b b}}_{22} | | | | ω ω | | {| |}^{22})) \frac{s the s}{| | | | s the s | | | |} - - - - - - ((1111))$

其中，k₁和k₂为设计的正常数，sgn(·)为符号函数，和分别是参数b₀、b₁和b₂的估计值，其在线更新律为：Among them, k ₁ and k ₂ are designed constants, sgn( ) is a sign function, and are the estimated values of parameters b ₀ , b ₁ and b ₂ respectively, and their online update law is:

$\{\begin{matrix} {\overset{\cdot &Center Dot;}{\overset{^^}{b b}}}_{00} = = \frac{| | | | s the s | | | |}{{c c}_{00}} \\ {\overset{\cdot \cdot}{\overset{^^}{b b}}}_{11} = = \frac{| | | | s the s | | | | | | | | ω ω | | | |}{{c c}_{11}} \\ {\overset{\cdot &Center Dot;}{\overset{^^}{b b}}}_{22} = = \frac{| | | | s the s | | | | | | | | ω ω | | {| |}^{22}}{{c c}_{22}} \end{matrix} - - - - - - ((1212))$

c₀、c₁和c₂为设计的正常数；c ₀ , c ₁ and c ₂ are designed constants;

最后，进行稳定性证明：Finally, a proof of stability:

选择：choose:

$V V = = \frac{11}{22} {s the s}^{T T} J J s the s + + \frac{{c c}_{00}}{22} {\overset{~ ~}{b b}}_{00}^{22} + + \frac{{c c}_{11}}{22} {\overset{~ ~}{b b}}_{11}^{22} + + \frac{{c c}_{22}}{22} {\overset{~ ~}{b b}}_{22}^{22} - - - - - - ((1313))$

其中， in,

对式(13)两边求导，得：Deriving both sides of formula (13), we get:

$\overset{\cdot \cdot}{V V} = = {s the s}^{T T} J J \overset{\cdot \cdot}{s the s} + + {c c}_{00} {\overset{~ ~}{b b}}_{00} {\overset{\cdot \cdot}{\overset{^^}{b b}}}_{00} + + {c c}_{11} {\overset{~ ~}{b b}}_{11} {\overset{\cdot \cdot}{\overset{^^}{b b}}}_{11} + + {c c}_{22} {\overset{~ ~}{b b}}_{22} {\overset{\cdot &Center Dot;}{\overset{^^}{b b}}}_{22} - - - - - - ((1414))$

将式(9)～(12)带入上式，并化简，得：Bring the formulas (9)~(12) into the above formula and simplify to get:

$\begin{matrix} \overset{\cdot \cdot}{V V} = = {s the s}^{T T} J J \overset{\cdot &Center Dot;}{s the s} - - {c c}_{00} {\overset{~ ~}{b b}}_{00} {\overset{\cdot \cdot}{\overset{^^}{b b}}}_{00} - - {c c}_{11} {\overset{~ ~}{b b}}_{11} {\overset{\cdot \cdot}{\overset{^^}{b b}}}_{11} - - {c c}_{22} {\overset{~ ~}{b b}}_{22} {\overset{\cdot \cdot}{\overset{^^}{b b}}}_{22} \\ = = {s the s}^{T T} [[- - {k k}_{11} {ασ ασ}_{e e} - - {k k}_{22} \frac{sgn sgn ((s the s))}{| | | | s the s | | | |} - - (({\overset{^^}{b b}}_{00} + + {\overset{^^}{b b}}_{11} | | | | ω ω | | | | + + {\overset{^^}{b b}}_{22} | | | | ω ω | | {| |}^{22})) \frac{s the s}{| | | | s the s | | | |} + + L L]] - - {c c}_{00} {\overset{~ ~}{b b}}_{00} {\overset{\cdot &Center Dot;}{\overset{^^}{b b}}}_{00} - - {c c}_{11} {\overset{~ ~}{b b}}_{11} {\overset{\cdot &Center Dot;}{\overset{^^}{b b}}}_{11} - - {c c}_{22} {\overset{~ ~}{b b}}_{22} {\overset{\cdot &Center Dot;}{\overset{^^}{b b}}}_{22} \\ \leq \leq - - {k k}_{11} α α | | | | s the s | | | | | | | | {σ σ}_{e e} | | | | - - {k k}_{22} \\ \leq \leq - - {k k}_{22} < < 00 \end{matrix}$

因此，在控制律式(11)及参数自适应律式(12)的控制下，系统一致渐近稳定。Therefore, under the control of control law (11) and parameter adaptive law (12), the system is uniformly asymptotically stable.

所述步骤3)中，接管控制力矩的鲁棒分配的具体方法为：In the step 3), the specific method for taking over the robust distribution of the control moment is:

由于控制力矩由推力和系绳张力共同实现，且推力与张力均为严格受限，则：Since the control torque is realized jointly by the thrust and the tension of the tether, and both the thrust and the tension are strictly limited, then:

$\{\begin{matrix} 00 N N \leq \leq {F f}_{11 x x},, {F f}_{22 x x},, {F f}_{66 x x},, {F f}_{77 x x} \leq \leq {a a}_{11} N N \\ 00 N N \leq \leq {F f}_{33 y the y},, {F f}_{88 y the y} \leq \leq {a a}_{22} N N \\ 00 N N \leq \leq {F f}_{44 z z},, {F f}_{55 z z},, {F f}_{99 z z},, {F f}_{1010 z z} \leq \leq {a a}_{33} N N \\ 00 N N \leq \leq {F f}_{1111 z z},, {F f}_{1212 z z} \leq \leq {a a}_{44} N N \\ 00 N N \leq \leq {F f}_{1313 x x} \leq \leq {a a}_{55} N N \end{matrix} - - - - - - ((1515))$

设a＝[a₁ a₁ a₂ a₃ a₃ a₁ a₁ a₂ a₃ a₃ a₄ a₄ a₅]，0为13×1的零矩阵；式(15)表示为：0≤F≤a；Let a=[a ₁ a ₁ a ₂ a ₃ a ₃ a ₁ a ₁ a ₂ a ₃ a ₃ a ₄ a ₄ a ₅ ], 0 is a 13×1 zero matrix; formula (15) is expressed as: 0≤ F≤a;

利用鲁棒分配方法将步骤2)计算的控制力矩T分配到真实的控制执行量，即12个推力器的推力和系绳张力上，具体方法如下：Use the robust distribution method to distribute the control torque T calculated in step 2) to the real control execution quantity, that is, the thrust of the 12 thrusters and the tether tension. The specific method is as follows:

3-1)以燃料消耗最少为目标函数，将控制分配问题转化为以下的鲁棒优化问题。3-1) Taking the minimum fuel consumption as the objective function, transform the control assignment problem into the following robust optimization problem.

目标函数：min([1 1 1 1 1 1 1 1 1 1 1 1 0]F)＝min(W^TF)；Objective function: min([1 1 1 1 1 1 1 1 1 1 1 0]F)=min(W ^T F);

约束：T＝DF，0≤F≤a；Constraints: T=DF, 0≤F≤a;

令将等式约束转化为不等式约束；make Convert equality constraints into inequality constraints;

约束：HF≥N，0≤F≤a；Constraints: HF≥N, 0≤F≤a;

利用鲁棒优化理论，将优化问题重写为：Using robust optimization theory, the optimization problem can be rewritten as:

$\{\begin{matrix} min min (({W W}^{T T} F f)) \\ s the s . . t t . . {h h}_{i i} F f &GreaterEqual; &Greater Equal; {n no}_{i i} \\ 00 \leq \leq F f \leq \leq a a \end{matrix},, &ForAll; &ForAll; {h h}_{i i} &Element; &Element; {Ξ ξ}_{i i},, &ForAll; &ForAll; i i = = 11 ... ... 66 - - - - - - ((1616))$

其中，h_i为包含不确定性的矩阵H的第i行，且在不确定集Ξ_i中取值；不确定集Ξ_i可用椭球不确定性描述，即：Among them, h _i is the i-th row of the matrix H containing uncertainty, and takes a value in the uncertain set Ξ _i ; the uncertain set Ξ _i can be described by ellipsoidal uncertainty, namely:

${Ξ ξ}_{i i} = = {{{h h}_{i i} | | {h h}_{i i}^{T T} = = {\overset{&OverBar; &OverBar;}{h h}}_{i i}^{T T} + + {Θ Θ}_{i i} {u u}_{i i},, | | | | {u u}_{i i} | | | | \leq \leq ρ ρ}},, i i = = 11,, ... ... 66 - - - - - - ((1717))$

表示由测量或辨识得到的各行的标称值，Θ_i为与不确定性分布相关的对称正定或半正定矩阵，u_i为与不确定性相关的列向量，ρ为不确定性的欧几里得范数的上界； Indicates the nominal value of each row obtained by measurement or identification, Θ _i is a symmetric positive definite or semi-positive definite matrix related to the uncertainty distribution, u _i is a column vector related to the uncertainty, ρ is the Euclidean of the uncertainty The upper bound of the Reed norm;

3-2)利用椭球不确定性的特点，利用式(17)化简式(16)，并利用3-2) Using the characteristics of ellipsoidal uncertainty, use formula (17) to simplify formula (16), and use

min(x^TΘu_i)＝-ρ||Θx||min(x ^T Θu _i )=-ρ||Θx||

将鲁棒优化问题转化为锥二次优化问题：Transform the robust optimization problem into a cone quadratic optimization problem:

$\{\begin{matrix} m m i i n no (({W W}^{T T} F f)) \\ s the s . . t t . . \overset{&OverBar; &OverBar;}{{h h}_{i i}} F f - - ρ ρ | | | | {Θ Θ}_{i i} F f | | | | &GreaterEqual; &Greater Equal; {n no}_{i i} \\ 00 \leq \leq F f \leq \leq a a \end{matrix},, &ForAll; &ForAll; i i = = 11 ... ... 66 - - - - - - ((1818))$

最后，利用内点法求解上述锥优化问题。Finally, the interior point method is used to solve the above cone optimization problem.

与现有技术相比，本发明具有以下有益效果：Compared with the prior art, the present invention has the following beneficial effects:

本发明采用基于空间绳系机器人的系绳推力器对空间非合作目标星进行姿态联合接管控制方法，可充分利用系绳张力，节省接管控制过程中的化学推进剂消耗。在国内外系绳与推力器联合对目标姿态控制的研究中，是将目标惯量视为已知，且未考虑控制量分配、控制量受约束等问题，使得其使用范围与可靠性大大降低。采用自适应姿态控制和力矩的鲁棒分配方法，充分考虑了非合作目标的惯量未知、质心未知、操作机构抓捕点未知等特性，以及受限状态量及控制量，使得系统能够在线实时获得未知参数，且避免了受限状态量及控制量对系统的影响，极大提高了其实际使用范围与可靠性。The present invention adopts the tether thruster based on the space tether robot to carry out attitude joint takeover control method on the space non-cooperative target star, which can make full use of the tension of the tether and save the chemical propellant consumption in the takeover control process. In the domestic and foreign research on the target attitude control of the combination of tether and thruster, the target inertia is regarded as known, and problems such as the distribution of control variables and the constraints of control variables are not considered, which greatly reduces its application range and reliability. Adaptive attitude control and torque robust distribution methods are adopted, fully considering the characteristics of non-cooperative targets such as unknown inertia, unknown center of mass, and unknown capture point of the operating mechanism, as well as limited state quantities and control quantities, so that the system can be obtained online in real time. Unknown parameters, and avoiding the influence of limited state quantities and control quantities on the system, greatly improving its practical application range and reliability.

【附图说明】【Description of drawings】

图1为空间绳系机器人目标抓捕示意图；Figure 1 is a schematic diagram of target capture by a space tethered robot;

图2为推力器的分布图；Figure 2 is a distribution diagram of the thruster;

图3为利用系绳/推力器的空间非合作目标姿态联合接管控制流程图。Fig. 3 is a flow chart of joint takeover control of space non-cooperative target attitude using tether/thruster.

其中，1-空间非合作目标星；2-空间绳系机器人的操作机构；3-空间绳系机器人的系绳；4-第1组操作机构；5-第2组操作机构；6-第3组操作机构；7-第4组操作机构。Among them, 1-space non-cooperative target star; 2-operating mechanism of space tethered robot; 3-tether of space tethered robot; 4-operating mechanism of the first group; 5-operating mechanism of the second group; 6-third Group operating mechanism; 7 - Group 4 operating mechanism.

【具体实施方式】【detailed description】

下面结合附图对本发明做进一步详细描述：The present invention is described in further detail below in conjunction with accompanying drawing:

参见图1-图3，本发明利用系绳推力器的空间非合作目标姿态联合接管控制方法，包括以下步骤：Referring to Fig. 1-Fig. 3, the present invention utilizes the space non-cooperative target posture joint takeover control method of the tether thruster, comprising the following steps:

步骤1：建立空间非合作目标星姿态接管控制模型Step 1: Establish a space non-cooperative target star attitude takeover control model

如图1所示，1是空间非合作目标星，2是空间绳系机器人的操作机构，3是空间绳系机器人的系绳。O_T为空间非合作目标星的质心，O_TX_TY_TZ_T为目标星本体系，O_G为操作机构的质心，O_GX_GY_GZ_G为操作机构本体系，O_C为系绳与操作机构的连接点。为简化建模过程，假设两个坐标系各坐标轴均相互平行。设操作机构质心O_G在目标星本体系O_TX_TY_TZ_T下的坐标为X_G＝[x_G,y_G,z_G]。As shown in Figure 1, 1 is the space non-cooperative target star, 2 is the operating mechanism of the space tethered robot, and 3 is the tether of the space tethered robot. O _T is the center of mass of the non-cooperative target star in space, O _T X _T Y _T Z _T is the system of the target star, O _G is the center of mass of the operating mechanism, O _G X _G Y _G Z _G is the system of the operating mechanism, and O _C is The point of attachment of the tether to the operating mechanism. To simplify the modeling process, it is assumed that the coordinate axes of the two coordinate systems are parallel to each other. Let the coordinates of the center of mass O _G of the operating mechanism under the target star system O _T X _T Y _T Z _T be X _G =[x _G ,y _G ,z _G ].

如图2所示，第1组操作机构4、第2组操作机构5、第3组操作机构6与第4组操作机构7共十二个推力器，且呈“十”字安装。第1组操作机构4与第2组操作机构5包含五个正交安装的推力器，第3组操作机构6与第4组操作机构7各为一个推力器。As shown in Figure 2, the first group of operating mechanisms 4, the second group of operating mechanisms 5, the third group of operating mechanisms 6 and the fourth group of operating mechanisms 7 have a total of twelve thrusters, and are installed in the shape of "ten". The first group of operating mechanisms 4 and the second group of operating mechanisms 5 include five orthogonally installed thrusters, and the third group of operating mechanisms 6 and the fourth group of operating mechanisms 7 each have one thruster.

设每个推力器的推力范围为[0 a]N，则，十二个推力器在操作机构本体系产生的推力及在操作机构本体系的作用点位置为：Assuming that the thrust range of each thruster is [0 a]N, then, the thrust generated by the twelve thrusters in the system of the operating mechanism and the position of the action point in the system of the operating mechanism are:

第一组：First group:

第二组：Second Group:

第三组及第四组Group 3 and Group 4

由于空间绳系机器人的系绳可达数百米，而在接管控制中，目标星姿态运动造成的系绳方向改变较小，为简化建模过程，可假设其方向不变且沿操作机构本体系-x方向。因此，设系绳最大拉力为a₅N，系绳拉力及作用点在操作机构本体系下可表示为：Since the tether of a space tethered robot can reach hundreds of meters, and in the takeover control, the direction of the tether caused by the attitude movement of the target star changes little. In order to simplify the modeling process, it can be assumed that its direction remains unchanged and along System - x direction. Therefore, assuming that the maximum tension of the tether is a ₅ N, the tension and action point of the tether can be expressed as:

由于操作对象为非合作目标，所以陀螺等测量装置，推力器/系绳等执行机构均安装于空间绳系机器人的操作机构上，因此，在操作机构本体系下，建立空间非合作目标性的姿态动力学方程为：Since the operating object is a non-cooperative target, measuring devices such as gyroscopes, and actuators such as thrusters/tethers are all installed on the operating mechanism of the space tethered robot. Therefore, under the operating mechanism system, a space non-cooperative target The attitude dynamic equation is:

其中，J为目标星转动惯量矩阵，ω为目标星的角速度，^×为叉乘算子，T_d为干扰力矩，T＝T_c+T_t为控制力矩。T_c为推力器产生的控制力矩Among them, J is the moment of inertia matrix of the target star, ω is the angular velocity of the target star, ^× is the cross product operator, T _d is the disturbance torque, and T=T _c +T _t is the control torque. T _c is the control torque generated by the thruster

T_t为系绳产生的控制力矩T _t is the control torque generated by the tether

T_t＝(X_G+X₅)×F₁₃ (3)T _t =(X _G +X ₅ )×F ₁₃ (3)

则控制力矩T可化简为：Then the control torque T can be simplified as:

其中，D为控制量分配矩阵，F为执行器组成的列向量。Among them, D is the control quantity allocation matrix, and F is the column vector composed of actuators.

$\overset{\cdot &Center Dot;}{σ σ} = = G G ((σ σ)) ω ω - - - - - - ((55))$

其中，σ为目标星的姿态修正罗德里格斯参数，I₃为3×3的单位矩阵。Among them, σ is the attitude correction Rodrigues parameter of the target star, and I ₃ is a 3×3 identity matrix.

设非合作目标星的期望姿态为σ_d，期望角速度为ω_d，则，目标星姿态误差动力学/运动学方程为：Suppose the expected attitude of the non-cooperative target star is σ _d , and the expected angular velocity is ω _d , then the dynamics/kinematics equation of the attitude error of the target star is:

$\{\begin{matrix} {\overset{\cdot &Center Dot;}{σ σ}}_{e e} = = G G (({σ σ}_{e e})) {ω ω}_{e e} \\ J J {\overset{\cdot &Center Dot;}{ω ω}}_{e e} = = - - {((ω ω))}^{\times \times} J J ((ω ω)) - - {Jω Jω}_{d d} + + T T + + {T T}_{d d} \end{matrix} - - - - - - ((77))$

式中，表示MRP乘法。In the formula, Indicates MRP multiplication.

步骤2：设计非合作目标星的姿态自适应接管控制律Step 2: Design the attitude adaptive takeover control law of the non-cooperative target star

由于推力矩和系绳张力矩构成了冗余控制系统，且各推力和系绳张力均为受约束量，直接以推力和张力为控制量设计控制器十分复杂，因此，采用姿态接管控制律和控制分配律分开设计的方法。Since the thrust moment and the tether tension moment constitute a redundant control system, and each thrust and tether tension are constrained quantities, it is very complicated to design the controller directly using the thrust and tension as the control quantities. Therefore, the attitude takeover control law and A method for separate design of control distribution laws.

在姿态接管控制律的设计中，由于非合作目标的转动惯量未知，需要设计自适应的姿态接管控制律。In the design of attitude takeover control law, since the moment of inertia of the non-cooperative target is unknown, it is necessary to design an adaptive attitude takeover control law.

首先，定义辅助误差变量：s＝ω_e+ασ_e。则First, an auxiliary error variable is defined: s=ω _e +ασ _e . but

$\begin{matrix} J J \overset{\cdot \cdot}{s the s} = = J J {\overset{\cdot \cdot}{ω ω}}_{e e} + + J J α α {\overset{\cdot &Center Dot;}{σ σ}}_{e e} \\ = = - - {((ω ω))}^{\times \times} J J ((ω ω)) - - {Jω Jω}_{d d} + + T T + + {T T}_{d d} + + α α J J G G (({σ σ}_{e e})) {ω ω}_{e e} \\ = = T T + + L L \end{matrix} - - - - - - ((99))$

其中，L＝-(ω)×J(ω)-[J+αJG(σ_e)]ω_d+T_d+αJG(σ_e)ω。用||·||表示矢量的欧几里得范数，下面对||L||进行分析。Wherein, L=-(ω)×J(ω)-[J+αJG(σ _e )]ω _d +T _d +αJG(σ _e )ω. Use ||·|| to represent the Euclidean norm of the vector, and analyze ||L|| below.

由于ω_d有界。设外部扰动T_d的欧几里得范数满足||T_d||≤c_d0+c_d1||ω||²，c_d0和c_d1均为未知且非负的常数。则：because _ωd is bounded. Assuming that the Euclidean norm of the external disturbance T _d satisfies ||T _d ||≤c _d0 +c _d1 ||ω|| ² , both c _d0 and c _d1 are unknown and non-negative constants. but:

其中，b₀、b₁和b₂均为未知且非负的常数。Wherein, b ₀ , b ₁ and b ₂ are all unknown and non-negative constants.

其中，k₁，k₂为设计的正常数，sgn(·)为符号函数，和分别是参数b₀、b₁和b₂的估计值，其在线更新律为：Among them, k ₁ and k ₂ are designed constants, sgn( ) is a sign function, and are the estimated values of parameters b ₀ , b ₁ and b ₂ respectively, and their online update law is:

$\{\begin{matrix} {\overset{\cdot &Center Dot;}{\overset{^^}{b b}}}_{00} = = \frac{| | | | s the s | | | |}{{c c}_{00}} \\ {\overset{\cdot &Center Dot;}{\overset{^^}{b b}}}_{11} = = \frac{| | | | s the s | | | | | | | | ω ω | | | |}{{c c}_{11}} \\ {\overset{\cdot &Center Dot;}{\overset{^^}{b b}}}_{22} = = \frac{| | | | s the s | | | | | | | | ω ω | | {| |}^{22}}{{c c}_{22}} \end{matrix} - - - - - - ((1212))$

c₀，c₁和c₂为设计的正常数。c ₀ , c ₁ and c ₂ are designed constants.

最后，进行稳定性证明：Finally, a proof of stability:

选择：choose:

其中， in,

对式(13)两边求导，得：Deriving both sides of formula (13), we get:

$\overset{\cdot &Center Dot;}{V V} = = {s the s}^{T T} J J \overset{\cdot &Center Dot;}{s the s} + + {c c}_{00} {\overset{~ ~}{b b}}_{00} {\overset{\cdot &Center Dot;}{\overset{^^}{b b}}}_{00} + + {c c}_{11} {\overset{~ ~}{b b}}_{11} {\overset{\cdot &Center Dot;}{\overset{^^}{b b}}}_{11} + + {c c}_{22} {\overset{~ ~}{b b}}_{22} {\overset{\cdot &Center Dot;}{\overset{^^}{b b}}}_{22} - - - - - - ((1414))$

$\begin{matrix} \overset{\cdot &Center Dot;}{V V} = = {s the s}^{T T} J J \overset{\cdot &Center Dot;}{s the s} - - {c c}_{00} {\overset{~ ~}{b b}}_{00} {\overset{\cdot &Center Dot;}{\overset{^^}{b b}}}_{00} - - {c c}_{11} {\overset{~ ~}{b b}}_{11} {\overset{\cdot \cdot}{\overset{^^}{b b}}}_{11} - - {c c}_{22} {\overset{~ ~}{b b}}_{22} {\overset{\cdot \cdot}{\overset{^^}{b b}}}_{22} \\ = = {s the s}^{T T} [[- - {k k}_{11} {ασ ασ}_{e e} - - {k k}_{22} \frac{sgn sgn ((s the s))}{| | | | s the s | | | |} - - (({\overset{^^}{b b}}_{00} + + {\overset{^^}{b b}}_{11} | | | | ω ω | | | | + + {\overset{^^}{b b}}_{22} | | | | ω ω | | {| |}^{22})) \frac{s the s}{| | | | s the s | | | |} + + L L]] - - {c c}_{00} {\overset{~ ~}{b b}}_{00} {\overset{\cdot \cdot}{\overset{^^}{b b}}}_{00} - - {c c}_{11} {\overset{~ ~}{b b}}_{11} {\overset{\cdot \cdot}{\overset{^^}{b b}}}_{11} - - {c c}_{22} {\overset{~ ~}{b b}}_{22} {\overset{\cdot &Center Dot;}{\overset{^^}{b b}}}_{22} \\ \leq \leq - - {k k}_{11} α α | | | | s the s | | | | | | | | {σ σ}_{e e} | | | | - - {k k}_{22} \\ \leq \leq - - {k k}_{22} < < 00 \end{matrix}$

步骤3：接管控制力矩的鲁棒分配Step 3: Robust distribution of takeover control moments

由于控制力矩由推力和系绳张力共同实现，且推力与张力均为严格受限。Since the control torque is jointly realized by the thrust and the tension of the tether, and both the thrust and the tension are strictly limited.

设a＝[a₁ a₁ a₂ a₃ a₃ a₁ a₁ a₂ a₃ a₃ a₄ a₄ a₅]，0为13×1的零矩阵。上式可表示为：0≤F≤a。Let a=[a ₁ a ₁ a ₂ a ₃ a ₃ a ₁ a ₁ a ₂ a ₃ a ₃ a ₄ a ₄ a ₅ ], 0 is a 13×1 zero matrix. The above formula can be expressed as: 0≤F≤a.

另外，由于操作机构质心O_G在目标星本体系下的坐标不确定，导致推力与系绳张力作用点在目标星本体系下的坐标均不确定，因此，本步骤利用鲁棒分配方法将步骤2计算的控制力矩T分配到真实的控制执行量：十二个推力器的推力和系绳张力上。In addition, since the coordinates of the center of mass O _G of the operating mechanism in the target star system are uncertain, the coordinates of the thrust and tether tension action points in the target star system are uncertain. Therefore, this step uses the robust assignment method to divide the step 2. The calculated control torque T is distributed to the actual control performance: the thrust of the twelve thrusters and the tension of the tether.

首先，以燃料消耗最少为目标函数，将控制分配问题转化为以下的鲁棒优化问题。First, with the minimum fuel consumption as the objective function, the control assignment problem is transformed into the following robust optimization problem.

约束：T＝DF，0≤F≤a。Constraints: T=DF, 0≤F≤a.

令将等式约束转化为不等式约束，make Transform equality constraints into inequality constraints,

约束：HF≥N，0≤F≤a。Constraints: HF≥N, 0≤F≤a.

其中，h_i为包含不确定性的矩阵H的第i行，且在不确定集Ξ_i中取值。不确定集Ξ_i可用椭球不确定性描述，即：Among them, h _i is the i-th row of the matrix H containing uncertainty, and takes values in the uncertain set Ξ _i . Uncertainty set Ξ _i can be described by ellipsoidal uncertainty, namely:

表示由测量或辨识得到的各行的标称值，Θ_i为与不确定性分布相关的对称正定或半正定矩阵，u_i为与不确定性相关的列向量，ρ为不确定性的欧几里得范数的上界。 Indicates the nominal value of each row obtained by measurement or identification, Θ _i is a symmetric positive definite or semi-positive definite matrix related to the uncertainty distribution, u _i is a column vector related to the uncertainty, ρ is the Euclidean of the uncertainty The upper bound of the Reed norm.

然后，利用椭球不确定性的特点，利用式(17)化简式(16)，并利用Then, using the characteristics of ellipsoidal uncertainty, use formula (17) to simplify formula (16), and use

min(x^TΘu_i)＝-ρ||Θx||min(x ^T Θu _i )=-ρ||Θx||

将鲁棒优化问题转化为锥二次优化问题。Transform the robust optimization problem into a cone quadratic optimization problem.

内点法详细步骤详见:DAVID G,LUENBERGER,YINYU YE.Linear and NonlinearProgramming[M].Third edition.Berlin:Springer Verlag,2008:111–140.For detailed steps of the interior point method, see: DAVID G, LUENBERGER, YINYU YE. Linear and Nonlinear Programming [M]. Third edition. Berlin: Springer Verlag, 2008: 111–140.

以上内容仅为说明本发明的技术思想，不能以此限定本发明的保护范围，凡是按照本发明提出的技术思想，在技术方案基础上所做的任何改动，均落入本发明权利要求书的保护范围之内。The above content is only to illustrate the technical idea of the present invention, and cannot limit the protection scope of the present invention. Any changes made on the basis of the technical solution according to the technical idea proposed in the present invention, all fall into the scope of the claims of the present invention. within the scope of protection.

Claims

1. Utilize the space non-cooperative target posture joint takeover control method of tether thruster, it is characterized in that, comprises the following steps:

1) Establish a space non-cooperative target star attitude takeover control model;

2) Design the attitude adaptive takeover control law of the non-cooperative target star;

3) Take over the robust distribution of control moments.

2. the space non-cooperative target attitude joint takeover control method utilizing tether thruster according to claim 1, is characterized in that, in described step 1), the concrete method of setting up the space non-cooperative target star attitude takeover control model is as follows :

Take O _T as the center of mass of the non-cooperative target star in space, establish the target star system O _T X _T Y _T Z _T , take O _G as the center of mass of the operating mechanism, establish the operating mechanism system O _G X _G Y _G Z _G , O _C is the connection point between the tether and the operating mechanism; in order to simplify the modeling process, it is assumed that the coordinate axes of the two coordinate systems are parallel to each other, and the center of mass O _G of the operating mechanism is located at the target star system O _T X _T Y _T Z _T The coordinates are X _G =[x _G , y _G , z _G ];

Four sets of operating mechanisms, a total of 12 thrusters are installed in the shape of a "ten"; among them, the first set of operating mechanisms (4) and the second set of operating mechanisms (5) include 5 orthogonally installed thrusters, and the third set of operating mechanisms The mechanism (6) and the fourth group of operating mechanism (7) are each a thruster;

Assuming that the thrust range of each thruster is [0a]N, the thrust generated by the 12 thrusters in the system of the operating mechanism and the position of the action point in the system of the operating mechanism are:

First group:

Second Group:

The third and fourth groups:

In order to simplify the modeling process, it is assumed that its direction remains unchanged and is along the -x direction of the operating mechanism itself; therefore, the maximum tension of the tether is a ₅ N, and the tension and action point of the tether are expressed in the operating mechanism itself as:

Since the operating object is a non-cooperative target, the measurement device and the actuator are installed on the operating mechanism of the space tethered robot. Therefore, under the system of the operating mechanism, the attitude dynamic equation of the non-cooperative target in space is established as:

J J \overset{\cdot &Center Dot;}{ω ω} + + {ω ω}^{\times \times} J J ω ω = = T T + + {T T}_{d d} - - - - - - ((11))

Among them, J is the moment of inertia matrix of the target star, ω is the angular velocity of the target star, × is the cross product operator, T _d is the disturbance torque, T=T _c +T _t is the control torque, T _c is the control torque generated by the thruster :

{T T}_{c c} = = {Σ Σ}_{i i = = 11}^{55} (({X x}_{G G} + + {X x}_{11})) \times \times {F f}_{i i} + + {Σ Σ}_{i i = = 66}^{1010} (({X x}_{G G} + + {X x}_{22})) \times \times {F f}_{i i} + + (({X x}_{G G} + + {X x}_{33})) \times \times {F f}_{1111} + + (({X x}_{G G} + + {X x}_{44})) \times \times {F f}_{1212} - - - - - - ((22))

F _i is the thrust corresponding to the ith thruster, i is the label of the thruster, and T _t is the control torque generated by the tether:

T _t =(X _G +X ₅ )×F ₁₃ (3)

Then the control torque T is simplified as:

T T = = {T T}_{c c} + + {T T}_{t t} = = D D. F f = = {[\begin{matrix} 00 & (({z z}_{G G} + + {z z}_{11})) & - - (({y the y}_{G G} + + {y the y}_{11})) \\ 00 & - - (({z z}_{G G} + + {z z}_{11})) & (({y the y}_{G G} + + {y the y}_{11})) \\ (({z z}_{G G} + + {z z}_{11})) & 00 & - - (({x x}_{G G} + + {x x}_{11})) \\ (({y the y}_{G G} + + {y the y}_{11})) & - - (({x x}_{G G} + + {x x}_{11})) & 00 \\ - - (({y the y}_{G G} + + {y the y}_{11})) & (({x x}_{G G} + + {x x}_{11})) & 00 \\ 00 & (({z z}_{G G} + + {z z}_{22})) & - - (({y the y}_{G G} + + {y the y}_{22})) \\ 00 & - - (({z z}_{G G} + + {z z}_{22})) & (({y the y}_{G G} + + {y the y}_{22})) \\ - - (({z z}_{G G} + + {z z}_{22})) & 00 & (({x x}_{G G} + + {x x}_{22})) \\ (({y the y}_{G G} + + {y the y}_{22})) & - - (({x x}_{G G} + + {x x}_{22})) & 00 \\ - - (({y the y}_{G G} + + {y the y}_{22})) & (({x x}_{G G} + + {x x}_{22})) & 00 \\ - - (({y the y}_{G G} + + {y the y}_{33})) & (({x x}_{G G} + + {x x}_{33})) & 00 \\ (({y the y}_{G G} + + {y the y}_{33})) & - - (({x x}_{G G} + + {x x}_{33})) & 00 \\ 00 & - - (({z z}_{G G} + + {z z}_{55})) & (({y the y}_{G G} + + {y the y}_{55})) \end{matrix}]}^{T T} [\begin{matrix} {F f}_{11 x x} \\ {F f}_{22 x x} \\ {F f}_{33 y the y} \\ {F f}_{44 z z} \\ {F f}_{55 z z} \\ {F f}_{66 x x} \\ {F f}_{77 x x} \\ {F f}_{88 y the y} \\ {F f}_{99 z z} \\ {F f}_{1010 z z} \\ {F f}_{1111 z z} \\ {F f}_{1212 z z} \\ {F f}_{1313 x x} \end{matrix}] - - - - - - ((44))

Among them, D is the control quantity allocation matrix, and F is the column vector composed of actuators;

The attitude kinematic equation of the target star described by the modified Rodriguez parameters is:

\overset{\cdot \cdot}{σ σ} = = G G ((σ σ)) ω ω - - - - - - ((55))

G G ((σ σ)) = = \frac{11}{44} [[((11 - - {σ σ}^{T T} σ σ)) {I I}_{33} + + 22 {σ σ}^{\times \times} + + 22 {σσ σσ}^{T T}]] - - - - - - ((66))

Among them, σ is the attitude correction Rodrigues parameter of the target star, and I ₃ is a 3×3 identity matrix;

Suppose the expected attitude of the non-cooperative target star is σ _d , and the expected angular velocity is ω _d , then the dynamics/kinematics equation of the attitude error of the target star is:

\{\begin{matrix} {\overset{\cdot &Center Dot;}{σ σ}}_{e e} = = G G (({σ σ}_{e e})) {ω ω}_{e e} \\ J J {\overset{\cdot &Center Dot;}{ω ω}}_{e e} = = - - {((ω ω))}^{\times \times} J J ((ω ω)) - - {Jω Jω}_{d d} + + T T + + {T T}_{d d} \end{matrix} - - - - - - ((77))

Among them, σ _e is the attitude error, ω _e is the angular velocity error, and the expressions of the two are:

\{\begin{matrix} {σ σ}_{e e} = = σ σ &CircleTimes; &CircleTimes; {σ σ}_{d d}^{- - 11} = = \frac{((11 - - {σ σ}_{d d}^{T T} {σ σ}_{d d})) σ σ + + (({σ σ}^{T T} σ σ - - 11)) {σ σ}_{d d} - - 22 {σ σ}_{d d} \times \times σ σ}{11 + + (({σ σ}_{d d}^{T T} {σ σ}_{d d})) (({σ σ}^{T T} σ σ)) + + 22 {σ σ}_{d d}^{T T} σ σ} \\ {ω ω}_{e e} = = ω ω - - {ω ω}_{d d} \end{matrix} - - - - - - ((88))

In formula (8), Indicates MRP multiplication.

3. the space non-cooperative target attitude joint takeover control method utilizing tether thruster according to claim 1, is characterized in that, in described step 2), the attitude adaptive takeover control law method of designing non-cooperative target star for:

First, define the auxiliary error variable: s=ω _e +ασ _e , α≥0, then

\begin{matrix} J J \overset{\cdot \cdot}{s the s} = = J J {\overset{\cdot \cdot}{ω ω}}_{e e} + + J J α α {\overset{\cdot &Center Dot;}{σ σ}}_{e e} \\ = = - - {((ω ω))}^{\times \times} J J ((ω ω)) - - {Jω Jω}_{d d} + + T T + + {T T}_{d d} + + α α J J G G (({σ σ}_{e e})) {ω ω}_{e e} \\ = = T T + + L L \end{matrix} - - - - - - ((99))

Among them, L=-(ω) ^× J(ω)-[J+αJG(σ _e )]ω _d +T _d +αJG(σ _e )ω; use |||| Number, analyze ||L||:

because ω _d is bounded; suppose the Euclidean norm of external disturbance T _d satisfies ||T _d ||≤c _d0 +c _d1 ||ω|| ² , c _d0 and c _d1 are both unknown and non-negative constants ,but:

||L||≤b ₀ +b ₁ ||ω||+b ₂ ||ω|| ² (10)

Among them, b ₀ , b ₁ and b ₂ are all unknown and non-negative constants;

Then, on this basis, the attitude adaptive control law is designed:

T T = = - - {k k}_{11} {ασ ασ}_{e e} - - {k k}_{22} \frac{sgn sgn ((s the s))}{| | | | s the s | | | |} - - (({\overset{^^}{b b}}_{00} + + {\overset{^^}{b b}}_{11} | | | | ω ω | | | | + + {\overset{^^}{b b}}_{22} | | | | ω ω | | {| |}^{22})) \frac{s the s}{| | | | s the s | | | |} - - - - - - ((1111))

Among them, k ₁ and k ₂ are designed constants, sgn( ) is a sign function, and are the estimated values of parameters b ₀ , b ₁ and b ₂ respectively, and their online update law is:

\{\begin{matrix} {\overset{\cdot &Center Dot;}{\overset{^^}{b b}}}_{00} = = \frac{| | | | s the s | | | |}{{c c}_{00}} \\ {\overset{\cdot &Center Dot;}{\overset{^^}{b b}}}_{11} = = \frac{| | | | s the s | | | | | | | | ω ω | | | |}{{c c}_{11}} \\ {\overset{\cdot &Center Dot;}{\overset{^^}{b b}}}_{22} = = \frac{| | | | s the s | | | | | | | | ω ω | | {| |}^{22}}{{c c}_{22}} \end{matrix} - - - - - - ((1212))

c ₀ , c ₁ and c ₂ are designed constants;

Finally, a proof of stability:

choose:

V V = = \frac{11}{22} {s the s}^{T T} J J s the s + + \frac{{c c}_{00}}{22} {\overset{~ ~}{b b}}_{00}^{22} + + \frac{{c c}_{11}}{22} {\overset{~ ~}{b b}}_{11}^{22} + + \frac{{c c}_{22}}{22} {\overset{~ ~}{b b}}_{22}^{22} - - - - - - ((1313))

in,

Deriving both sides of formula (13), we get:

\overset{\cdot &Center Dot;}{V V} = = {s the s}^{T T} J J \overset{\cdot \cdot}{s the s} + + {c c}_{00} {\overset{~ ~}{b b}}_{00} {\overset{\cdot &Center Dot;}{\overset{^^}{b b}}}_{00} + + {c c}_{11} {\overset{~ ~}{b b}}_{11} {\overset{\cdot &Center Dot;}{\overset{^^}{b b}}}_{11} + + {c c}_{22} {\overset{~ ~}{b b}}_{22} {\overset{\cdot &Center Dot;}{\overset{^^}{b b}}}_{22} - - - - - - ((1414))

Bring the formulas (9)~(12) into the above formula and simplify to get:

\begin{matrix} \overset{\cdot \cdot}{V V} = = {s the s}^{T T} J J \overset{\cdot \cdot}{s the s} - - {c c}_{00} {\overset{~ ~}{b b}}_{00} {\overset{\cdot \cdot}{\overset{^^}{b b}}}_{00} - - {c c}_{11} {\overset{~ ~}{b b}}_{11} {\overset{\cdot \cdot}{\overset{^^}{b b}}}_{11} - - {c c}_{22} {\overset{~ ~}{b b}}_{22} {\overset{\cdot \cdot}{\overset{^^}{b b}}}_{22} \\ = = {s the s}^{T T} [[- - {k k}_{11} {ασ ασ}_{e e} - - {k k}_{22} \frac{sgn sgn ((s the s))}{| | | | s the s | | | |} - - (({\overset{^^}{b b}}_{00} + + {\overset{^^}{b b}}_{11} | | | | ω ω | | | | + + {\overset{^^}{b b}}_{22} | | | | ω ω | | {| |}^{22})) \frac{s the s}{| | | | s the s | | | |} + + L L]] - - {c c}_{00} {\overset{~ ~}{b b}}_{00} {\overset{\cdot \cdot}{\overset{^^}{b b}}}_{00} - - {c c}_{11} {\overset{~ ~}{b b}}_{11} {\overset{\cdot \cdot}{\overset{^^}{b b}}}_{11} - - {c c}_{22} {\overset{~ ~}{b b}}_{22} {\overset{\cdot \cdot}{\overset{^^}{b b}}}_{22} \\ \leq \leq - - {k k}_{11} α α | | | | s the s | | | | | | | | {σ σ}_{e e} | | | | - - {k k}_{22} \\ \leq \leq - - {k k}_{22} < < 00 \end{matrix}

Therefore, under the control of control law (11) and parameter adaptive law (12), the system is uniformly asymptotically stable.

4. The space non-cooperative target attitude joint takeover control method utilizing tether thrusters according to claim 1, characterized in that, in the step 3), the specific method for taking over the robust distribution of the control torque is:

Since the control torque is realized jointly by the thrust and the tension of the tether, and both the thrust and the tension are strictly limited, then:

\{\begin{matrix} 00 N N \leq \leq {F f}_{11 x x},, {F f}_{22 x x},, {F f}_{66 x x},, {F f}_{77 x x} \leq \leq {a a}_{11} N N \\ 00 N N \leq \leq {F f}_{33 y the y},, {F f}_{88 y the y} \leq \leq {a a}_{22} N N \\ 00 N N \leq \leq {F f}_{44 z z},, {F f}_{55 z z},, {F f}_{99 z z},, {F f}_{1010 z z} \leq \leq {a a}_{33} N N \\ 00 N N \leq \leq {F f}_{1111 z z},, {F f}_{1212 z z} \leq \leq {a a}_{44} N N \\ 00 N N \leq \leq {F f}_{1313 x x} \leq \leq {a a}_{55} N N \end{matrix} - - - - - - ((1515))

Let a=[a ₁ a ₁ a ₂ a ₃ a ₃ a ₁ a ₁ a ₂ a ₃ a ₃ a ₄ a ₄ a ₅ ], 0 is a 13×1 zero matrix; formula (15) is expressed as: 0≤ F≤a;

Use the robust distribution method to distribute the control torque T calculated in step 2) to the real control execution quantity, that is, the thrust of the 12 thrusters and the tether tension. The specific method is as follows:

3-1) With the minimum fuel consumption as the objective function, the control allocation problem is transformed into the following robust optimization problem;

Objective function: min([1 1 1 1 1 1 1 1 1 1 1 0]F)=min(W ^T F);

Constraints: T=DF, 0≤F≤a;

make Convert equality constraints into inequality constraints;

Constraints: HF≥N, 0≤F≤a;

Using robust optimization theory, the optimization problem can be rewritten as:

\{\begin{matrix} min min (({W W}^{T T} F f)) \\ s the s . . t t . . {h h}_{i i} F f &GreaterEqual; &Greater Equal; {n no}_{i i} \\ 00 \leq \leq F f \leq \leq a a \end{matrix},, &ForAll; &ForAll; {h h}_{i i} &Element; &Element; {Ξ ξ}_{i i},, &ForAll; &ForAll; i i = = 11 ... ... 66 - - - - - - ((1616))

Among them, h _i is the i-th row of the matrix H containing uncertainty, and takes a value in the uncertain set Ξ _i ; the uncertain set Ξ _i can be described by ellipsoidal uncertainty, namely:

{Ξ ξ}_{i i} = = {{{h h}_{i i} | | {h h}_{i i}^{T T} = = {\overset{&OverBar; &OverBar;}{h h}}_{i i}^{T T} + + {Θ Θ}_{i i} {u u}_{i i},, | | | | {u u}_{i i} | | | | \leq \leq ρ ρ}},, i i = = 11,, ... ... 66 - - - - - - ((1717))

Indicates the nominal value of each row obtained by measurement or identification, Θ _i is a symmetric positive definite or semi-positive definite matrix related to the uncertainty distribution, u _i is a column vector related to the uncertainty, ρ is the Euclidean of the uncertainty The upper bound of the Reed norm;

3-2) Using the characteristics of ellipsoidal uncertainty, use formula (17) to simplify formula (16), and use

min(x ^T Θu _i )=-ρ||Θx||

Transform the robust optimization problem into a cone quadratic optimization problem:

\{\begin{matrix} m m i i n no (({W W}^{T T} F f)) \\ s the s . . t t . . {\overset{&OverBar; &OverBar;}{h h}}_{i i} F f - - ρ ρ | | | | {Θ Θ}_{i i} F f | | | | &GreaterEqual; &Greater Equal; {n no}_{i i} \\ 00 \leq \leq F f \leq \leq a a \end{matrix},, &ForAll; &ForAll; i i = = 11 ... ... 66 - - - - - - ((1818))

Finally, the interior point method is used to solve the above cone optimization problem.