CN105022402A

CN105022402A - Method for determining shortest time of coupled rigid-body spacecraft rapid maneuver

Info

Publication number: CN105022402A
Application number: CN201510515288.0A
Authority: CN
Inventors: 耿云海; 黄思萌; 侯志立; 李东柏; 叶东; 陈雪芹; 张刚; 方向; 李海勤; 史明明
Original assignee: Harbin Institute of Technology
Current assignee: Harbin Institute of Technology
Priority date: 2015-08-20
Filing date: 2015-08-20
Publication date: 2015-11-04
Anticipated expiration: 2035-08-20
Also published as: CN105022402B

Abstract

The invention relates to a method for determining the shortest time of coupled rigid-body spacecraft rapid maneuver, and aims to solve problems of small effective operating range and long maneuvering time of a non-contact actuator of an existing undisturbed load satellite. The method is implemented through the following technical scheme which comprises the steps of 1, establishing a load platform coordinate system O<s>x<a>y<a>z<a> and a service platform coordinate system Oxyz, and marking the load platform coordinate system O<s>x<a>y<a>z<a> and the service platform coordinate system Oxyz as an Sa system and an Sb system respectively; 2, writing rotation inertia matrixes of a load platform and a service platform in regards to a system mass center of the coupled rigid-body spacecraft; 3, writing an attitude kinematics equation and an angular momentum conservation equation of the coupled rigid-body spacecraft; 4, calculating an Euler axis e and a rotation angle Phi<f>; 5, writing expressions of the angular acceleration Phi<..>(t), the angular speed Phi<.>(t) and the angle degree Phi(t); 6, writing expressions of an attitude quaternion q<m0> and an attitude quaternion q<m> of the load platform, an attitude matrix C<ao> of the load platform , an attitude matrix C<bo> of the service platform, the attitude angular speed Omega<al><a> of the load platform, the attitude angular speed Omega<bl> of the service platform, the attitude angular acceleration Omega<.><al><a> of the load platform and the attitude angular acceleration Omega<.><bl><a> of the service platform; 7, acquiring T<e><a>, T<w> and H<w> in regards to Phi<..>max, Phi<.>max and t; and 8, solving the constrained shortest maneuvering time by using a Matlab optimization toolbox according to the rotation angle Phi<f>, the T<e><a>, the T<w> and the H<w>. The method provided by the invention is applied to the field of spacecrafts.

Description

Method for determining shortest time of fast maneuver of dual-rigid-body spacecraft

Technical Field

The invention relates to a method for determining the shortest time of rapid maneuvering of a dual-rigid-body spacecraft.

Background

The invention is provided for the rapid maneuver of the satellite without disturbance load. The concept of "undisturbed loading" satellites is proposed by nelson pedreior and applied to satellites with high precision pointing and high stability control requirements. The satellite is a double rigid body spacecraft, which is composed of a load platform and a service platform, wherein a non-contact actuator controls the attitude of the load platform, an additional executing mechanism (such as a reaction wheel and the like) controls the attitude of the service platform, and the non-contact actuator can isolate the additional executing mechanism and the vibration of the external environment interference acting on the service platform, so that the effective load can realize high-precision pointing and high-stability control. However, since the effective working range of the contactless actuator is only a few millimeters, the attitude of the service platform must track the attitude of the load platform, and in the process of large-angle maneuvering, the service platform and the load platform are maneuvered as a whole, which is equivalent to maneuvering a single rigid body satellite, and the maneuvering time is mainly limited by an additional execution mechanism and is long. For an undisturbed load satellite carrying a large payload, the existing configuration cannot meet the requirement of quick maneuvering.

Disclosure of Invention

The invention provides a method for determining the shortest time for the quick maneuvering of a double-rigid-body spacecraft, which aims to solve the problems that the effective working range and maneuvering time of a non-contact actuator of the existing undisturbed load satellite are long, and the quick maneuvering of the undisturbed load satellite carrying a large effective load cannot be met.

The above-mentioned invention purpose is realized through the following technical scheme:

step one, establishing a load platform coordinate system O_sx_ay_az_aAnd service platform coordinate system O_bx_by_bz_bThe coordinate system of the load platform is denoted as S_aThe coordinate system of the service platform is marked as S_bWherein O is_sLocated in the center of the spherical hinge, O_bLocated in the center of mass of the service platform, O_aIs the center of mass of the load platform, O_cThe center of mass of the dual rigid spacecraft system is located at the origin of coordinates of a load platform coordinate system_sLoad platform and garmentThe service platform forms a dual rigid body spacecraft, and the load platform is connected with the service platform through a spherical hinge;

step two, according to the S obtained in the step one_aSystem and S_bWriting a rotational inertia matrix of a load platform and a service platform about a mass center of a dual rigid spacecraft system;

writing an attitude kinematics equation of the dual rigid spacecraft and an angular momentum conservation equation of the dual rigid spacecraft according to the rotational inertia matrix of the load platform and the service platform obtained in the step two, which is relative to the system centroid of the dual rigid spacecraft;

step four, calculating the Euler axis e and the rotation angle phi of the load platform from the initial attitude maneuver to the target attitude_f；

Step five, obtaining the rotation angle phi according to the step four_fWriting angular acceleration of the load platform tracking trajectoryAngular velocityAnd an expression for the angle Φ (t);

sixthly, according to the Euler axis e obtained in the fourth step and the angular acceleration of the tracking track of the load platform obtained in the fifth stepAngular velocityAnd an expression of the angle phi (t) is used for writing a quaternion q of the attitude of the load platform_m0And q is_mAttitude matrix C of load platform_aoAttitude matrix C of service platform_boAttitude angular velocity of load platformAttitude angular velocity of service platformAttitude angular acceleration of a load platformAnd attitude angular acceleration of the service platformThe expression of (1);

step seven, the step fiveAnd Φ (t), and C in step six_ao、C_bo、Andsubstituting into the attitude dynamics equation of the dual rigid body spacecraft and the angular momentum conservation equation of the dual rigid body spacecraft in the step three to obtain the equation aboutAnd of tAnd

step eight, obtaining the rotation angle phi according to the step four_fStep sevenAndthe shortest maneuver time with constraints was solved using the Matlab optimization toolkit.

Effects of the invention

The invention provides a double-rigid-body spacecraft attitude control system for disaster emergency monitoring, which is characterized in that the double-rigid-body spacecraft is composed of a load platform and a service platform, wherein the load platform carries a payload, the service platform carries an actuating mechanism, and the load platform and the service platform are connected through a spherical hinge. The significance of the research on the dual rigid body spacecraft is as follows: (1) the load platform can carry more payload; (2) the actuating mechanism of the double-rigid-body spacecraft is provided with the motor and the flywheel, and compared with a single-rigid-body spacecraft with the same mass and rotational inertia, the double-rigid-body spacecraft has higher maneuvering speed; (3) the load platform is separated from the service platform, so that the influence of the vibration of the actuating mechanism on the effective load can be reduced. Since one of the main tasks of the dual rigid body spacecraft is to maneuver the payload platform carrying the payload quickly, there is no requirement on the attitude of the service platform carrying the actuators. The invention selects the condition that the loading platform is quickly maneuvered and the service platform keeps the orientation to the ground.

The method has the advantages that the rapid maneuvering of the dual rigid body spacecraft is realized, the spherical hinge driven by the motor is added between the load platform and the service platform, the limitation of the effective working range of the non-contact actuator is removed, and the load platform and the service platform can perform relative attitude motion with a larger angle; by introducing two time-varying rotational inertia matrixes, a detailed attitude dynamics equation of the dual rigid body spacecraft is given, by introducing reasonable hypothesis, two sub-rigid bodies with serious coupling are decoupled, expressions of a target function and a constraint function of the time optimal problem are given, the shortest maneuvering time and the corresponding maximum angular acceleration and maximum angular velocity can be conveniently solved by using a Matlab optimization tool box, in the process of large-angle attitude maneuver of the load platform, as the attitude of the service platform does not need to be tracked, namely, the whole satellite is not required to be maneuvered, only the load platform part is maneuvered, the maneuvering time can be greatly shortened, the prior art needs to move the load platform and the service platform simultaneously, and the quick maneuvering method provided by the patent can shorten the maneuvering time by 50% on the basis of the prior art on the assumption that the quality of the load platform is close to that of the service platform. The invention selects the conditions that the load platform is quickly maneuvered and the service platform keeps the orientation to the ground, and meets the problem of quick maneuvering of undisturbed load satellites carrying large-scale effective loads.

Drawings

FIG. 1 is a flow chart of the present invention;

FIG. 2 is a schematic diagram of the coordinate system in the second embodiment, wherein O_EIs the center of mass of the earth, O_cIs the center of mass, O, of the dual rigid body spacecraft system_aIs the center of mass of the load platform, O_bAs the center of mass of the service platform, O_sIs the center of mass of the spherical hinge, [ i_a j_a k_a]^TIs S_aCoordinate basis of system, i_aIs S_aZ-axis of system, j_aIs S_aX-axis of the system, k_aIs S_aThe y-axis of the system, T is transposed, [ i ]_b j_b k_b]^TIs S_bCoordinate basis of system, i_bIs S_bX-axis of the system, j_bIs S_bY-axis of the system, k_bIs S_bZ-axis of system, dm_aIs a load platform mass infinitesimal dm_bAs a service platform quality element, R_aIs composed of O_EPoint to O_aVector of (2), R_bIs composed of O_EPoint to O_bVector of (A), R_cIs composed of O_EPoint to O_cVector of (a), r_aIs composed of O_EDirection dm_aVector of (a), r_bIs composed of O_EDirection dm_bVector of (d)₁Is composed of O_sPoint to O_aVector of (d)₂Is composed of O_bPoint to O_sVector of (a), p₁Is composed of O_aPoint to O_cVector of (a), p₂Is composed of O_bPoint to O_cVector of (a), q₁Is composed of O_sDirection dm_aVector of (a), q₂Is composed of O_sDirection dm_bThe vector of (a);

FIG. 3 is a schematic diagram of a track traced by the loading platform according to the sixth embodiment, where t₀As the moment of start of maneuver, t₁For the acceleration end time, t₂At the end of the uniform speed, t_fIn order to be the time of the end of the maneuver,the angular velocity of the trajectory is tracked for the load platform,the maximum angular acceleration of the tracked trajectory for the load platform,the maximum angular velocity of the tracking trajectory for the load platform,tracking angular acceleration of the trajectory for the load platform;

FIG. 4 is a graph of the attitude angular acceleration of the loading platform illustrated in example 1, in degrees/sec;

FIG. 5 is a graph of the torque modulus of the motor shown in example 1, wherein Nm is Nm;

FIG. 6 is a graph showing the moment module value of the flywheel shown in embodiment 1;

FIG. 7 is a graph showing the angular momentum of the flywheel shown in embodiment 1.

Detailed Description

The first embodiment is as follows: the embodiment is described with reference to fig. 1, and the method for determining the shortest time for the fast maneuver of the dual rigid body spacecraft specifically comprises the following steps:

step one, establishing a load platform coordinate system O_sx_ay_az_aAnd service platform coordinate system O_bx_by_bz_bThe coordinate system of the load platform is denoted as S_aThe coordinate system of the service platform is marked as S_bWherein O is_sLocated in the center of the spherical hinge, O_bLocated in the center of mass of the service platform, O_aIs the center of mass of the load platform, O_cThe center of mass of the dual rigid spacecraft system is located at the origin of coordinates of a load platform coordinate system_sThe load platform and the service platform form a double rigid body spacecraft, and are connected through a spherical hinge;

step seven, based on a zero momentum system, neglecting the disturbance moment, and combining the step fiveAnd Φ (t), and C in step six_ao、C_bo、Andsubstituting into the attitude dynamics equation of the dual rigid body spacecraft and the angular momentum conservation equation of the dual rigid body spacecraft in the step three to obtain the equation aboutAnd of tAnd

The second embodiment is as follows: the present embodiment is described with reference to fig. 2, and the present embodiment is different from the first embodiment in that: establishing a load platform coordinate system O in the step one_sx_ay_az_aAnd service platform coordinate system O_bx_by_bz_bThe coordinate system of the load platform is denoted as S_aThe coordinate system of the service platform is marked as S_bWherein O is_sLocated in the center of the spherical hinge, O_bLocated in the center of mass of the service platform, O_aIs the center of mass of the load platform, O_cThe center of mass of the dual rigid spacecraft system is located at the origin of coordinates of a load platform coordinate system_sThe load platform and the service platform form a double rigid body spacecraft, and are connected through a spherical hinge; the specific process is as follows:

establishing a load platform coordinate system O_sx_ay_az_aAnd service platform coordinate system O_bx_by_bz_bLoad platform coordinate system O_sx_ay_az_aIs marked as S_aThe coordinate system of the service platform is marked as S_bWherein O is_sIs the center of the spherical hinge, O_bAs the center of mass, x, of the service platform_aIs a load platform coordinate system x-axis, y_aIs the y-axis, z, of the load platform coordinate system_aIs a z-axis, x, of a coordinate system of the load platform_bAs a service platform coordinate system xAxis, y_bAs the service platform coordinate system y-axis, z_bServing as a z axis of a coordinate system of the service platform; o is_aIs the center of mass of the load platform, O_cThe coordinate origin of the coordinate system of the loading platform is not positioned at O for the mass center of the dual rigid body spacecraft system and the attitude kinetic equation of the dual rigid body spacecraft is convenient to be subsequently derived_aIs located at O_s。

Other steps and parameters are the same as those in the first embodiment.

The third concrete implementation mode: the present embodiment differs from the first or second embodiment in that: s obtained in the step two according to the step one_aSystem and S_bWriting a rotational inertia matrix of a load platform and a service platform about a mass center of a dual rigid spacecraft system; the specific process is as follows:

load platform with respect to O_cThe angular momentum vector of (a) is:

in the formula, dm_aIs a micro-element of mass of the load platform, q₁Is composed of O_sDirection dm_aVector of (a), p₁Is composed of O_aPoint to O_cVector of (v)_aIIs dm_aThe absolute velocity vector of (a) is,is O_bAbsolute velocity vector of (1)₁For load platforms with respect to O_sInertial dyadic of (H)_aFor load platforms with respect to O_cAngular momentum vector of d₁Is composed of O_sPoint to O_aVector of (a), ω_aIIs S_aAbsolute angular velocity vector of the system, ω_bIIs S_bAbsolute angular velocity vector of the system, d₂Is composed of O_sPoint to O_bA vector of (a);

service platform with respect to O_cThe angular momentum vector of (a) is:

in the formula, dm_bAs quality elements of the service platform, q₂Is composed of O_bDirection dm_bVector of (a), p₂Is composed of O_bPoint to O_cVector of (v)_bIIs dm_bAbsolute velocity vector of (1)₂For service platform with respect to O_bInertial dyadic of (H)_bFor service platform with respect to O_cAngular momentum vector of, omega_bIIs S_bAn absolute angular velocity vector of the system;

double rigid body spacecraft system with respect to O_cThe total angular momentum of (a) is:

in the formula,is O_bAbsolute velocity vector of (1), H_wIs the angular momentum vector of the flywheel, H is the dual rigid body spacecraft system with respect to O_cThe angular momentum vector of (a);

because m is_ap₁+m_bp₂Is equal to 0, and p₂-p₁＝d₁+d₂Therefore, it is

p_{1} = - \frac{m_{b}}{m_{a} + m_{b}} (d_{1} + d_{2}) - - - (29)

p_{2} = \frac{m_{a}}{m_{a} + m_{b}} (d_{1} + d_{2}) - - - (30)

By substituting formula (29) and formula (30) for formula (28), a

In the formula, E is a unit inertial vector;

load platform and service platform with respect to O_cThe inertial vectors of (a) are respectively:

in the formula I_aFor load platforms with respect to O_cInertial dyadic of (I)_bFor service platform with respect to O_cThe inertial dyadic of (c);

then the formula (31) can be expressed as

H＝I_a·ω_aI+I_b·ω_bI+H_w (34)

I_aAt S_aThe component matrix under the system is the load platform with respect to O_cThe moment of inertia matrix of (a):

in the formula,for load platforms with respect to O_cThe matrix of the moment of inertia of (a),for load platforms with respect to O_sThe rotational inertia matrix of m_aMass of the load platform, m_bIn order to provide the quality of the service platform,is composed of O_sPoint to O_aThe component array of the vector of (a),is composed of O_sPoint to O_bComponent array of vectors of (3), C_abIs S_aIs relative to S_bAttitude matrix of system, C_baIs S_bIs relative to S_aThe attitude matrix of the system is determined,is composed ofThe cross-multiplication matrix of (a) is,is composed ofA cross-product matrix of;

I_bat S_bThe component matrix under the system is the service platform with respect to O_cThe moment of inertia matrix of (a):

in the formula, the superscripts a and b are vectors or vectors in the direction of S_aSystem and S_bAn array or matrix of components under the system,for service platform with respect to O_cThe matrix of the moment of inertia of (a),for service platform with respect to O_bA rotational inertia matrix of;

and isAndrespectively, of first order derivatives of

In the formula,is S_aAbsolute angular velocity vector of the system is at S_aAn array of components under the system is provided,is S_bAbsolute angular velocity vector of the system is at S_bAn array of components under the system is provided,is composed ofThe cross-multiplication matrix of (a) is,is composed ofCross-product matrix of (a).

Other steps and parameters are the same as those in the first or second embodiment.

The fourth concrete implementation mode: the present embodiment differs from the first, second or third embodiment in that: writing an attitude kinematics equation of the dual rigid body spacecraft and an angular momentum conservation equation of the dual rigid body spacecraft according to the rotational inertia matrix of the load platform and the service platform obtained in the second step in the third step on the mass center of the dual rigid body spacecraft system; the specific process is as follows:

writing an attitude kinematics equation and an angular momentum conservation equation of the dual rigid body spacecraft according to the rotational inertia matrix of the load platform and the service platform about the system centroid of the dual rigid body spacecraft, which is obtained in the step two:

the attitude kinematic equation of the dual rigid body spacecraft is shown in formulas (3) and (4):

the angular momentum conservation equation of the dual rigid body spacecraft is shown as the formula (5):

in the formula,is composed ofThe derivative of (a) of (b),is composed ofThe derivative of (a) of (b),is composed ofThe derivative of (a) of (b),is composed ofThe upper corner mark o is a component array or a component matrix of the vector or the vector parallel under the orbit coordinate system of the dual rigid body spacecraft,is S_aThe component array of the absolute angular velocity vector of the system,is S_bComponent array of absolute angular velocity vectors of the system, C_aoIs S_aIs the attitude matrix of the relative orbit system,is a coordinate array of the motor moment vector,is a coordinate array of the moment vector of the flywheel,is a component array of disturbance moment vectors acting on the load platform,is a component array of disturbance moment vectors acting on the dual rigid body spacecraft system,is an array of components of the flywheel angular momentum vector,is a component array of angular momentum vectors of a dual rigid body spacecraft system, mu is a gravitational constant,is a component array of vectors pointing from the centroid to the center of mass of the load platform,is a component array of vectors pointing from the centroid to the centroid of the dual rigid-body spacecraft system, R_cIs composed ofOf a mold of R_aIs composed ofThe die of (a) is used,is composed ofThe cross-multiplication matrix of (a) is,is composed ofA cross-product matrix of;

load platform around O_aThe kinematic equation of the rotating posture is as follows:

in the formula,as a vector or dyadic at S_aDerivative of system, T_eAs motor torque vector, T_baMoment vector, T, acting on load platform for service platform_daDisturbance moment vector, omega, acting on the load platform_aIIs S_aAn absolute angular velocity vector of the system;

resultant force acting on the load platform force F acting on the load platform by the service platform_baAnd the interference force F acted on the load platform by the external environment_daComposition according to Newton's second law, having

F_{b a} + F_{d a} = m_{a} \frac{{d_{I}}^{2} R_{a}}{{dt}^{2}} = m_{a} \frac{{d_{I}}^{2} (R_{c} - p_{1})}{{dt}^{2}} - - - (43)

In the formula,as derivatives of vectors or dyadics in the inertial system, R_aTo point to O from the earth center_aVector of (2), R_cTo point to O from the earth center_cVector of (a), p₁Is composed of O_aPoint to O_cA vector of (a);

based on a two-body system of earth-spacecraft, having

Wherein μ is an earth gravity constant; | R_cL is R_cA modulus value of (d);

because F_daIs gravity, so take

Wherein, | R_aL is R_aA modulus value of (d);

by substituting formula (29), formula (44) and formula (45) for formula (43), the compound is obtained

In the formula,as a vector or dyadic at S_bA derivative of the system;

then will T_ba＝-d₁×F_baSubstitution of formula (42) to obtain a load platform winding O_aKinematic equation of attitude of rotation:

the above formula is at S_aIs represented by the following formula

In the formula,is composed ofThe cross-multiplication matrix of (a) is,is composed ofThe cross-multiplication matrix of (a) is,is S_aAbsolute angular velocity vector of the system is at S_aAn array of components under the system is provided,is S_bAbsolute angular velocity vector of the system is at S_bAn array of components under the system is provided,is composed ofCross multiplication moment ofThe number of the arrays is determined,is composed ofThe cross-multiplication matrix of (a) is,is a component array of a vector pointing to the center of mass of the loading platform from the center of the spherical hinge,is a component array of vectors pointing from the center of the spherical hinge to the center of mass of the service platform,is composed ofThe derivative of (a) of (b),is composed ofThe derivative of (a) of (b),for motor torque vector at S_aAn array of components under the system is provided,for disturbance torque vector at S_aA component array under the array;

derivation is carried out on the formula (34) to obtain a double rigid system winding O_cKinematic equation of attitude of rotation:

in the formula,T_was moment vector of flywheel, T_dFor acting on disturbance moment vector H of dual rigid body spacecraft system_wIs a flywheel angular momentum vector, omega_aIIs S_aAbsolute angular velocity vector of the system, ω_bIIs S_bAbsolute angular velocity vector of the system, H_wIs the angular momentum vector of the flywheel, I_aFor load platforms with respect to O_cInertial dyadic of (I)_bFor service platform with respect to O_cThe inertial dyadic of (c);

formula (49) at S_bThe following component formula:

in the formula, C_baIs S_bIs relative to S_aThe attitude matrix of the system is determined,is I_aAt S_aA matrix of the components of the image data,is I_bAt S_bA matrix of the components of the image data,is T_wAt S_bAn array of components under the system is provided,is T_dAt S_bAn array of components under the system is provided,is composed ofThe derivative of (a) of (b),is composed ofThe derivative of (a) of (b),is H_wAt S_bA component array under the array;

formula (34) at S_bIs represented by the following formula

In the formula,the total angular momentum vector of the dual rigid body spacecraft is at S_bA component array under the array;

other steps and parameters are the same as those in the first, second or third embodiment.

The fifth concrete implementation mode: the difference between this embodiment and the first, second, third or fourth embodiment is that: calculating the Euler axis e and the rotation angle phi of the load platform from the initial attitude maneuver to the target attitude in the fourth step_f(ii) a The specific process is as follows:

Φ_f＝2arccosq_m0 (6)

in the formula, q_m0Quaternion Q for maneuvering load platform from initial attitude to target attitude_mMark part of (a), q_mQuaternion Q for maneuvering load platform from initial attitude to target attitude_mSagittal portion of, Q_m＝[q_m0 q_m]^TIs a four-dimensional vector with the expression:

<math> <mrow> <msub> <mi>Q</mi> <mi>m</mi> </msub> <mo>=</mo> <msup> <msub> <mi>Q</mi> <mn>0</mn> </msub> <mo>*</mo> </msup> <mo>&CircleTimes;</mo> <msub> <mi>Q</mi> <mi>f</mi> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>8</mn> <mo>)</mo> </mrow> </mrow> </math>

in the formula, Q₀Is the initial attitude quaternion, Q, of the load platform_fIs a target attitude quaternion, Q, of the load platform_mQuaternions for the target pose, transposes the quaternions,for quaternion multiplication, T is the transpose of the array;

other steps and parameters are the same as those in the first, second, third or fourth embodiments.

The sixth specific implementation mode: the present embodiment is described with reference to fig. 3, and the present embodiment is different from the first, second, third, fourth, or fifth embodiment in that: the corner phi obtained in the step five according to the step four_fWriting angular acceleration of the load platform tracking trajectoryAngular velocityAnd an expression for the angle Φ (t); the specific process is as follows:

let phi (t)₀)＝0,Φ(t_f)＝Φ_f

In the formula,the angular acceleration of the trajectory is tracked for the load platform,the angular velocity of the track tracked by the load platform, phi (t) is the angle of the track tracked by the load platform,the maximum angular acceleration of the tracked trajectory for the load platform,maximum angular velocity, t, of the track for the load platform₀As the moment of start of maneuver, t₁For the acceleration end time, t₂At the end of the uniform speed, t_fT is time in seconds as the maneuvering ending time.

Other steps and parameters are the same as those in the first, second, third, fourth or fifth embodiment.

The seventh embodiment: the difference between this embodiment and the first, second, third, fourth, fifth or sixth embodiment is that: in the sixth step, the angular acceleration of the tracking track of the load platform obtained in the fifth step and the Euler axis e obtained in the fourth stepAngular velocityAnd an expression of the angle phi (t) is used for writing a quaternion q of the attitude of the load platform_m0And q is_mAttitude matrix C of load platform_aoAttitude matrix C of service platform_boAttitude angular velocity of load platformAttitude angular velocity of service platformAttitude angular acceleration of a load platformAnd attitude angular acceleration of the service platformThe expression of (1); the specific process is as follows:

assuming that the load platform tracks the track of the load platform, the service platform is stable;

then the platform attitude quaternion is loaded, as in equation (12) (13):

attitude matrix of the load platform, as in equation (14):

C_ao＝q_mq_m ^T+[q_m0E-(q_m)^×]² (14)

attitude angular velocity of the load platform, as in equation (15):

attitude angular acceleration of the load platform, as in equation (16):

the attitude matrix of the service platform is as shown in formula (17):

C_bo＝E (17)

attitude angular velocity of the service platform, as in equation (18):

attitude angular acceleration of the service platform, as in equation (19):

in the formula, q_m0Quaternion Q for maneuvering load platform from initial attitude to target attitude_mMark part of (a), q_mQuaternion Q for maneuvering load platform from initial attitude to target attitude_mSagittal portion of, C_boIs S_bAttitude matrix of the relative orbital system, C_obFor the track system to oppose S_bAn attitude matrix of the system, E is an identity matrix, E is an Euler axis of a tracking track of the load platform, q_m ^TIs q_mTranspose of (q)_m)^×Is q_mThe cross-multiplication matrix of (a) is,is a coordinate array of orbital angular velocity vectors in the spacecraft orbital system, e^×Is a cross-multiplication matrix of e, phi (t) is the angle of the load platform tracking track,the angular velocity of the trajectory is tracked for the load platform,for load platformAngular acceleration of the tracking track, C_boIs S_bIs relative to S_oA pose matrix of the system;

other steps and parameters are the same as those of the first, second, third, fourth, fifth or sixth embodiment.

The specific implementation mode is eight: the difference between this embodiment and the first, second, third, fourth, fifth, sixth or seventh embodiment is that: step seven is based on a zero momentum system, interference torque is ignored, and step five is carried outAnd Φ (t), and C in step six_ao、C_bo、Andsubstituting into the attitude dynamics equation of the dual rigid body spacecraft and the angular momentum conservation equation of the dual rigid body spacecraft in the step three to obtain the equation aboutAnd of tAndthe specific process is as follows:

q in the sixth step_m0And q is_mSubstitution into C_aoObtaining C for phi (t)_aoThen, mixing C_aoSubstitution intoAndin (1) get aboutAnd phi (t)And toAnd phi (t)Finally, C is put_ao、 C_bo、Andsubstituting into the attitude dynamics equation of the dual rigid body spacecraft and the angular momentum conservation equation of the dual rigid body spacecraft in the step three,can be usedAnd t represents;can be usedAnd t represents;can be used And t represents, get aboutAnd phi (t)And

in the formula,is a component array of the motor moment vector,is a component array of the flywheel moment vector,is a component array of the flywheel angular momentum vector;

wherein,maximum angular acceleration of a load platform tracking trajectoryA function of,Maximum angular velocity for tracking a trajectory for a load platformAs a function of (a) or (b),as a function of time t.

Other steps and parameters are the same as those of the first, second, third, fourth, fifth, sixth or seventh embodiments.

The specific implementation method nine: the difference between this embodiment and the first, second, third, fourth, fifth, sixth, seventh or eighth embodiment is that: the corner phi obtained in the step eight according to the step four_fStep sevenAndsolving the shortest maneuvering time containing constraints by using a Matlab optimization tool box; the specific process is as follows:

solving the minimum value of the constraint by using a Matlab optimization tool box, wherein the variable isAndthe objective function is maneuver time:

the constraint function is:

in the formula, T_emaxIs the minimum envelope radius of the motor torque, T_wmaxIs the minimum enveloping radius of the flywheel moment, H_wmaxIs the minimum enveloping radius of the angular momentum of the flywheel, phi_fIs the turning angle, deltat is the maneuvering time,is a component array of the motor moment vector,is a component array of the flywheel moment vector,is a component array of the flywheel angular momentum vector;

and obtaining the shortest maneuvering time according to the target function and the constraint function.

Other steps and parameters are the same as those of the first, second, third, fourth, fifth, sixth, seventh or eighth embodiments.

Examples

The beneficial effects of the invention are verified by adopting the following experiments:

example 1

The method for determining the shortest time for the rapid maneuver of the dual rigid body spacecraft is specifically carried out according to the following steps:

step seven, based on a zero momentum system, neglecting the disturbance moment, and combining the step fiveAnd Φ (t), and C in step six_ao、 C_bo、Andsubstituting into the attitude dynamics equation of the dual rigid body spacecraft and the angular momentum conservation equation of the dual rigid body spacecraft in the step three to obtain the equation aboutAnd of tAnd

step eight, obtaining the rotation angle phi according to the step four_fStep sevenAndsolving the shortest maneuvering time containing constraints by using a Matlab optimization tool box;

the rotational inertia matrixes of the load platform and the service platform are respectively

Mass of the load platform is m_a500kg, the mass of the service platform is m_b＝600kg。

d_{1}^{a} = {[\begin{matrix} 0 & 0 & 1 \end{matrix}]}^{T} m, d_{2}^{b} = {[\begin{matrix} 0 & 0 & 1 \end{matrix}]}^{T} m .

Angular velocity of the track omega_o0.0011rad/s, the position of the mass center of the load platform relative to the center of the earth is

The position of the mass center of the dual rigid body spacecraft system relative to the geocentric is

The maneuver starting time is t₀100s, the initial angular velocity of the load platform is

Target angular velocity of

The initial attitude of the loading platform is [ 000 ] to ground]^oTWith the target pose to ground [ 50712 ]]^oTThen the Euler axis is e ═ 0.96000.23000.1599]^TTarget turning angle of phi_f51.0603. The service platform keeps three-axis stability to the ground in the whole maneuvering process. The error of attitude angle measurement is three-axis 5 × 10^-4o(3 sigma), the attitude angular velocity measurement error is three-axis 10^-4oS (3. sigma.). The interference moments acting on the load platform and the dual rigid body spacecraft system are respectively

In the controller, the self-oscillation angular frequency omega is taken_n0.2rad/s, damping ratio ξ 0.9, then K_P＝ω_n ²＝0.04，K_D＝2ξω_n0.36. The flywheel adopts the four-oblique-installation structure, the maximum torque that the flywheel can provide is 0.4Nm, the maximum angular momentum is 32Nm multiplied by s, and the maximum torque that the motor can provide is 0.5 Nm.

According to the method of the invention, the maximum angular acceleration is determinedMaximum angular velocityThe maneuvering time Δ t is 151.8272 s. Simulation diagrams are shown in fig. 4, 5, 6 and 7;

as can be seen from the simulation diagrams of FIG. 4, FIG. 5, FIG. 6 and FIG. 7, the moment of the flywheel reaches the upper limit, and the moment of the motor and the angular momentum of the flywheel do not reach the upper limit, which is illustratedAndthe value of (1) satisfies the constraints of motor moment, flywheel moment and flywheel angular momentum, and the maneuvering time optimization method is feasible. The maneuver time cannot be made faster because the upper flywheel torque limit is relatively small.

Claims

1. A method for determining the shortest time of the rapid maneuver of a dual rigid body spacecraft is characterized in that the method for determining the shortest time of the rapid maneuver of the dual rigid body spacecraft is specifically carried out according to the following steps:

2. The method for determining the shortest time for a fast maneuver of a dual rigid body spacecraft as claimed in claim 1, wherein the first step is to establish a load platform coordinate system O_sx_ay_az_aAnd service platform coordinate system O_bx_by_bz_bThe coordinate system of the load platform is denoted as S_aThe coordinate system of the service platform is marked as S_bWherein O is_sLocated in the center of the spherical hinge, O_bLocated in the center of mass of the service platform, O_aIs the center of mass of the load platform, O_cThe center of mass of the dual rigid spacecraft system is located at the origin of coordinates of a load platform coordinate system_sThe load platform and the service platform form a double rigid body spacecraft, and are connected through a spherical hinge;

the specific process is as follows:

establishing a load platform coordinate system O_sx_ay_az_aAnd service platform coordinate system O_bx_by_bz_bLoad platform coordinate system O_sx_ay_az_aIs marked as S_aThe coordinate system of the service platform is marked as S_bWherein O is_sIs the center of the spherical hinge, O_bAs the center of mass, x, of the service platform_aIs a load platform coordinate system x-axis, y_aIs the y-axis, z, of the load platform coordinate system_aIs a z-axis, x, of a coordinate system of the load platform_bServing platform coordinate system x-axis, y_bAs the service platform coordinate system y-axis, z_bServing as a z axis of a coordinate system of the service platform; o is_aIs the center of mass of the load platform, O_cThe center of mass of the dual rigid spacecraft system is located at the origin of coordinates of a load platform coordinate system_s。

3. The method for determining the shortest time for a fast maneuver of a dual rigid body spacecraft as claimed in claim 2, wherein S obtained in the first step is used in the second step_aSystem and S_bWriting a rotational inertia matrix of a load platform and a service platform about a mass center of a dual rigid spacecraft system; the specific process is as follows:

load platform with respect to O_cThe angular momentum vector of (a) is:

in the formula, dm_aIs a micro-element of mass of the load platform, q₁Is composed of O_sDirection dm_aVector of (a), p₁Is composed of O_aPoint to O_cVector of (v)_aIIs dm_aThe absolute velocity vector of (a) is,is O_bThe absolute velocity vector of (a) is,for load platforms with respect to O_sInertial dyadic of (H)_aFor load platforms with respect to O_cAngular momentum vector of d₁Is composed of O_sPoint to O_aVector of (a), ω_aIIs S_aAbsolute angular velocity vector of the system, ω_bIIs S_bAbsolute angular velocity vector of the system, d₂Is composed of O_sPoint to O_bA vector of (a);

service platform with respect to O_cThe angular momentum vector of (a) is:

in the formula, dm_bAs quality elements of the service platform, q₂Is composed of O_bDirection dm_bVector of (a), p₂Is composed of O_bPoint to O_cVector of (v)_bIIs dm_bThe absolute velocity vector of (a) is,for service platform with respect to O_bInertial dyadic of (H)_bFor service platform with respect to O_cAngular momentum vector of, omega_bIIs S_bAn absolute angular velocity vector of the system;

p_{1} = - \frac{m_{b}}{m_{a} + m_{b}} (d_{1} + d_{2}) - - - (29)

p_{2} = \frac{m_{a}}{m_{a} + m_{b}} (d_{1} + d_{2}) - - - (30)

By substituting formula (29) and formula (30) for formula (28), a

In the formula,is unit inertial dyadic;

in the formula,for load platforms with respect to O_cThe inertial vector of (a) is,for service platform with respect to O_cThe inertial dyadic of (c);

then the formula (31) can be expressed as

At S_aThe component matrix under the system is the load platform with respect to O_cThe moment of inertia matrix of (a):

at S_bThe component matrix under the system is the service platform with respect to O_cThe moment of inertia matrix of (a):

and isAndrespectively, of first order derivatives of

4. The method for determining the shortest time for the rapid maneuver of the dual rigid body spacecraft according to the claim 3, wherein the attitude kinematics equation of the dual rigid body spacecraft and the angular momentum conservation equation of the dual rigid body spacecraft are written according to the rotational inertia matrix of the load platform and the service platform obtained in the step two about the centroid of the dual rigid body spacecraft system in the step three; the specific process is as follows:

F_{b a} + F_{d a} = m_{a} \frac{{d_{I}}^{2} R_{a}}{{dt}^{2}} = m_{a} \frac{{d_{I}}^{2} (R_{c} - p_{1})}{{dt}^{2}} - - - (43)

based on a two-body system of earth-spacecraft, having

Wherein μ is an earth gravity constant; | R_cL is R_cA modulus value of (d);

because F_daIs gravity, so take

Wherein, | R_aL is R_aA modulus value of (d);

In the formula,as a vector or dyadic at S_bA derivative of the system;

the above formula is at S_aIs tied downIs measured by

In the formula,is composed ofThe cross-multiplication matrix of (a) is,is composed ofThe cross-multiplication matrix of (a) is,is S_aAbsolute angular velocity vector of the system is at S_aAn array of components under the system is provided,is S_bAbsolute angular velocity vector of the system is at S_bAn array of components under the system is provided,is composed ofThe cross-multiplication matrix of (a) is,is composed ofThe cross-multiplication matrix of (a) is,is a component array of a vector pointing to the center of mass of the loading platform from the center of the spherical hinge,is a component array of vectors pointing from the center of the spherical hinge to the center of mass of the service platform,is composed ofThe derivative of (a) of (b),is composed ofThe derivative of (a) of (b),for motor torque vector at S_aAn array of components under the system is provided,for disturbance torque vector at S_aA component array under the array;

in the formula, T_wAs moment vector of flywheel, T_dFor acting on disturbance moment vector H of dual rigid body spacecraft system_wIs a flywheel angular momentum vector, omega_aIIs S_aAbsolute angular velocity vector of the system, ω_bIIs S_bAbsolute angular velocity vector of the system, H_wIs the angular momentum vector of the flywheel,for load platforms with respect to O_cThe inertial vector of (a) is,for service platform with respect to O_cThe inertial dyadic of (c);

formula (49) at S_bThe following component formula:

in the formula, C_baIs S_bIs relative to S_aThe attitude matrix of the system is determined,is composed ofAt S_aA matrix of the components of the image data,is composed ofAt S_bA matrix of the components of the image data,is T_wAt S_bAn array of components under the system is provided,is T_dAt S_bAn array of components under the system is provided,is composed ofThe derivative of (a) of (b),is composed ofThe derivative of (a) of (b),is H_wAt S_bA component array under the array;

formula (34) at S_bIs represented by the following formula

In the formula,the total angular momentum vector of the dual rigid body spacecraft is at S_bAn array of underlying components.

5. The method for determining the shortest time for the fast maneuver of a dual rigid body spacecraft as claimed in claim 4, wherein the fourth step is to calculate the Euler axis e and the rotation angle Φ of the load platform from the initial attitude to the target attitude_f(ii) a The specific process is as follows:

Φ_f＝2arccosq_m0 (6)

in the formula, Q₀Is the initial attitude quaternion, Q, of the load platform_fIs a target attitude quaternion, Q, of the load platform_mQuaternions for the target pose, transposes the quaternions,for quaternion multiplication, T is the transpose of the array.

6. The method for determining the shortest time for a fast maneuver of a dual rigid body spacecraft as claimed in claim 5, wherein the turning angle Φ obtained in the fifth step according to the fourth step_fWriting angular acceleration of the load platform tracking trajectoryAngular velocityAnd an expression for the angle Φ (t); the specific process is as follows:

let phi (t)₀)＝0,Φ(t_f)＝Φ_f

7. Root of herbaceous plantThe method for determining the shortest time for a fast maneuver of a dual rigid body spacecraft as claimed in claim 6, wherein the angular acceleration of the tracking trajectory of the loading platform obtained in the sixth step is obtained according to the Euler axis e obtained in the fourth step and the angular acceleration of the tracking trajectory of the loading platform obtained in the fifth stepAngular velocityAnd an expression of the angle phi (t) is used for writing a quaternion q of the attitude of the load platform_m0And q is_mAttitude matrix C of load platform_aoAttitude matrix C of service platform_boAttitude angular velocity of load platformAttitude angular velocity of service platformAttitude angular acceleration of a load platformAnd attitude angular acceleration of the service platformThe expression of (1); the specific process is as follows:

then the platform attitude quaternion is loaded, as in equation (12) (13):

attitude matrix of the load platform, as in equation (14):

C_ao＝q_mq_m ^T+[q_m0E-(q_m)^×]² (14)

attitude angular velocity of the load platform, as in equation (15):

attitude angular acceleration of the load platform, as in equation (16):

the attitude matrix of the service platform is as shown in formula (17):

C_bo＝E (17)

attitude angular velocity of the service platform, as in equation (18):

attitude angular acceleration of the service platform, as in equation (19):

in the formula, q_m0Quaternion Q for maneuvering load platform from initial attitude to target attitude_mMark part of (a), q_mQuaternion Q for maneuvering load platform from initial attitude to target attitude_mSagittal portion of, C_boIs S_bAttitude matrix of the relative orbital system, C_obFor the track system to oppose S_bAn attitude matrix of the system, E is an identity matrix, E is an Euler axis of a tracking track of the load platform, q_m ^TIs q_mTranspose of (q)_m)^×Is q_mThe cross-multiplication matrix of (a) is,is a coordinate array of orbital angular velocity vectors in the spacecraft orbital system, e^×Is a cross-multiplication matrix of e, phi (t) is the angle of the load platform tracking track,the angular velocity of the trajectory is tracked for the load platform,angular acceleration of the track for the load platform, C_boIs S_bIs relative to S_oAn attitude matrix of the system.

8. The method for determining the shortest time for a fast maneuver of a dual rigid body spacecraft of claim 7, wherein the seventh step is the fifth stepAnd Φ (t), and C in step six_ao、C_bo、Andsubstituting into the attitude dynamics equation of the dual rigid body spacecraft and the angular momentum conservation equation of the dual rigid body spacecraft in the step three to obtain the equation aboutAnd of tAndthe specific process is as follows:

q in the sixth step_m0And q is_mSubstitution into C_aoObtaining C for phi (t)_aoThen, mixing C_aoSubstitution intoAndin (1) get aboutAnd phi (t)And toAnd phi (t)Finally, C is put_ao、 C_bo、Andsubstituting into the attitude dynamics equation of the dual rigid body spacecraft and the angular momentum conservation equation of the dual rigid body spacecraft in the step three to obtain the equation aboutAnd phi (t)And

wherein,to be loadedMaximum angular acceleration of load platform tracking trackA function of,Maximum angular velocity for tracking a trajectory for a load platformAs a function of (a) or (b),as a function of time t.

9. The method for determining the shortest time for a fast maneuver of a dual rigid body spacecraft as claimed in claim 8, wherein the turning angle Φ obtained in step eight according to step four is determined_fStep sevenAndsolving the shortest maneuvering time containing constraints by using a Matlab optimization tool box; the specific process is as follows:

the constraint function is:

in the formula, T_emaxIs the minimum envelope radius of the motor torque, T_wmaxIs the minimum enveloping radius of the flywheel moment, H_wmaxIs the minimum enveloping radius of the angular momentum of the flywheel, phi_fIs the turning angle, Δ t is the maneuvering time,is a component array of the motor moment vector,is a component array of the flywheel moment vector,is a component array of the flywheel angular momentum vector;