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CN111891403B - Satellite attitude maneuver planning method - Google Patents

Satellite attitude maneuver planning method Download PDF

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CN111891403B
CN111891403B CN202010778383.0A CN202010778383A CN111891403B CN 111891403 B CN111891403 B CN 111891403B CN 202010778383 A CN202010778383 A CN 202010778383A CN 111891403 B CN111891403 B CN 111891403B
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刘刚
陈殿印
张泽涛
张文政
张家巍
叶立军
尹海宁
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Shanghai Aerospace Control Technology Institute
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Abstract

A satellite attitude maneuver planning method decomposes the maneuver of a satellite on a three-dimensional space into a plurality of rotations in one-dimensional directions by utilizing the relation between quaternions and three-dimensional rotations and the property of quaternion multiplication, plans a maneuver path with the initial and final angular velocities not equal to zero by adopting an analytic method aiming at the rotation in each one-dimensional direction obtained after decomposition, and performs quaternion operation and fusion on path planning results in all one-dimensional directions to obtain a final satellite attitude maneuver planning result. The method converts the nonlinear programming problem into a plurality of linear programming problems, can calculate the maneuvering target attitude at the current moment in real time in the satellite maneuvering process, guides the satellite to rapidly and stably complete the attitude maneuvering with the initial and final angular velocities not equal to zero, and provides the attitude programming result in an analytic form, so that the method has the advantages of little consumed computing resource, high reliability and suitability for on-orbit application.

Description

Satellite attitude maneuver planning method
Technical Field
The invention relates to a satellite real-time autonomous attitude maneuver planning method, in particular to a satellite attitude maneuver planning method with non-zero initial and final angular velocities.
Background
To accomplish different spatial tasks, the satellite needs to be transferred from one attitude to another, a process called attitude maneuver. At present, actuating mechanisms used for satellite attitude control comprise a reaction flywheel, a control moment gyroscope, an attitude control thruster and the like, and certain constraint conditions exist, so that in order to enable a satellite to quickly complete attitude maneuver under certain constraint conditions and quickly and stably start to execute tasks as soon as possible after the maneuver is completed, the attitude maneuver path of the satellite needs to be planned to guide the satellite to quickly and stably complete the maneuver.
At present, the initial and final angular velocities of a satellite are assumed to be zero by an attitude maneuver planning algorithm which can be used by the satellite in orbit, but in an actual task, after the satellite attitude maneuver is completed, a certain angular velocity may need to be maintained, so that the satellite needs to be maneuvered in place first and then the satellite angular velocity is accelerated to a specified size, and the transition time from the maneuvering completion to the task execution is remarkably increased. Therefore, if the satellite can be moved in place and the angular velocity can meet the requirements of the tasks, the time consumed by each task can be greatly shortened, and the capability of the satellite can be further improved. However, at present, the maneuvering planning algorithm capable of realizing the terminal angular velocity not being zero is realized by a nonlinear optimization algorithm or a large number of numerical iterative operations, although a certain optimality index can be reached, the calculation amount is too large, the occupied satellite calculation resources are too much, the consumed time is long, and the maneuvering planning algorithm basically does not have the condition of practical application in the prior art.
Disclosure of Invention
The invention provides a satellite attitude maneuver planning method, which decomposes rotation of a three-dimensional space by using the property of quaternion, converts a nonlinear planning problem into a plurality of linear planning problems, can calculate the maneuver target attitude at the current moment in real time in the satellite maneuver process, guides a satellite to rapidly and stably complete the attitude maneuver with the initial and final angular velocity not equal to zero, and provides an attitude planning result which has an analytic form, consumes few computing resources and has high reliability and is very suitable for on-orbit application.
In order to achieve the above object, the present invention provides a satellite attitude maneuver planning method, which is characterized in that a relationship between a quaternion and a three-dimensional rotation and the property of quaternion multiplication are utilized to decompose the maneuver of a satellite in a three-dimensional space into a plurality of rotations in one-dimensional directions, for each rotation in one-dimensional direction obtained after decomposition, an analytic method is adopted to plan a maneuver path with initial and final angular velocities not equal to zero, and quaternion operation fusion is performed on path planning results in all one-dimensional directions to obtain a final satellite attitude maneuver planning result.
The method for decomposing the maneuvering of the satellite on the three-dimensional space into the rotations in a plurality of one-dimensional directions comprises the following steps: target quaternion q for attitude maneuverfDecomposition into q0、q1、q2Three rotational quaternions;
Figure BDA0002619311570000021
wherein,
Figure BDA0002619311570000022
for quaternion multiplication, q1To complete the rotational quaternion from the satellite attitude to the target attitude, q2Rotational quaternion, q, for satellite acceleration to target angular velocity0Is a rotational quaternion to eliminate the effect of the initial angular velocity;
at any time t e [ t ] in the maneuvering processi,tf]The satellite-maneuvered instantaneous target quaternion q (t) is:
Figure BDA0002619311570000023
the instantaneous angular velocity of a satellite is decomposed into:
Figure BDA0002619311570000024
the method for planning the maneuvering path with the initial angular velocity and the final angular velocity not equal to zero comprises the following steps:
by planning q0Initial angular velocity ωiLowered to 0, and the rotational axis n of the rotation is obtained0And any time t epsilon [ t ] in the maneuvering processi,tf]Instantaneous angular velocity ω of0(t) and quaternion q0(t)；
Figure BDA0002619311570000025
Figure BDA0002619311570000026
Figure BDA0002619311570000031
q0(t)＝[cos(0.5θ0(t))n0xsin(0.5θ0(t))n0ysin(0.5θ0(t))n0zsin(0.5θ0(t))]T
By planning q2Accelerating a satellite to an angular velocity ωfDetermining the rotation axis n of the rotation2And any time t epsilon [ t ] in the maneuvering processi,tf]Instantaneous angular velocity ω of2(t) and quaternion q2(t)；
Figure BDA0002619311570000032
Figure BDA0002619311570000033
Figure BDA0002619311570000034
q2(t)＝[cos(0.5θ2(t))n0xsin(0.5θ2(t))n0ysin(0.5θ2(t))n0zsin(0.5θ2(t))]T；
By planning q1Taking satellite attitude from initial attitude qiRotate to target attitude qfDetermining the rotation axis e of the rotation1And any time t epsilon [ t ] in the maneuvering processi,tf]Instantaneous angular velocity ω of1(t) and quaternion q1(t)；
Figure BDA0002619311570000035
θ1(tf)＝2acos(q10)
Figure BDA0002619311570000036
q1Acceleration/deceleration time t corresponding to rotationaccAnd a uniform time tconstComprises the following steps:
Figure BDA0002619311570000037
Figure BDA0002619311570000038
angular velocity omega1(t) is:
Figure BDA0002619311570000039
instantaneous angle of rotation theta1(t) is:
Figure BDA0002619311570000041
corresponding instantaneous quaternion q1(t) is:
q1(t)＝[cos(0.5θ1(t))n0xsin(0.5θ1(t))n0ysin(0.5θ1(t))n0zsin(0.5θ1(t))]T。
the method for performing quaternion operation fusion on the path planning results in all one-dimensional directions comprises the following steps:
calculating the rotation quaternion q (t) and the angular speed after the synthesis at the current time t:
Figure BDA0002619311570000042
Figure BDA0002619311570000043
where [0, ω (t) ] is a pure four-element number consisting of a three-dimensional vector ω (t).
The method for decomposing the maneuvering of the satellite on the three-dimensional space into the rotations in a plurality of one-dimensional directions comprises the following steps: target quaternion q for attitude maneuverfDecomposition into q0、q1、q2Three rotational quaternions;
Figure BDA0002619311570000044
wherein,
Figure BDA0002619311570000045
for quaternion multiplication, q1To complete the rotational quaternion from the satellite attitude to the target attitude, q2Rotational quaternion, q, for acceleration of a satellite from an initial angular velocity to a target angular velocity0Is a rotational quaternion to calculate the effect of the initial angular velocity;
at any time t e [ t ] in the maneuvering processi,tf]The satellite-maneuvered instantaneous target quaternion q (t) is:
Figure BDA0002619311570000046
the instantaneous angular velocity of a satellite is decomposed into:
Figure BDA0002619311570000047
the method for planning the maneuvering path with the initial angular velocity and the final angular velocity not equal to zero comprises the following steps:
by planning q0Calculating the initial angular velocity omegaiShadow ofSounding to obtain the rotating axis n0And any time t epsilon [ t ] in the maneuvering processi,tf]Instantaneous angular velocity ω of0(t) and quaternion q0(t)；
Figure BDA0002619311570000051
ω0(t)＝ωi
Figure BDA0002619311570000052
q0(t)＝[cos(0.5θ0(t))n0xsin(0.5θ0(t))n0ysin(0.5θ0(t))n0zsin(0.5θ0(t))]T
By planning q2The angular velocity of the satellite is changed from omegaiAccelerate to omegafCalculate ωiAnd ωfThe angular velocity difference Δ ω therebetween;
Figure BDA0002619311570000053
from Δ ω to ω2(t) planning;
Figure BDA0002619311570000054
Figure BDA0002619311570000055
Figure BDA0002619311570000056
Figure BDA0002619311570000057
by planning q1Taking satellite attitude from initial attitude qiRotate to target attitude qfDetermining the rotation axis e of the rotation1And any time t epsilon [ t ] in the maneuvering processi,tf]Instantaneous angular velocity ω of1(t) and quaternion q1(t)；
Figure BDA0002619311570000058
θ1(tf)＝2acos(q10)
Figure BDA0002619311570000059
q1Acceleration/deceleration time t corresponding to rotationaccAnd a uniform time tconstComprises the following steps:
Figure BDA00026193115700000510
Figure BDA0002619311570000061
angular velocity omega1(t) is:
Figure BDA0002619311570000062
instantaneous angle of rotation theta1(t) is:
Figure BDA0002619311570000063
corresponding instantaneous quaternion q1(t) is:
q1(t)＝[cos(0.5θ1(t))n0xsin(0.5θ1(t))n0ysin(0.5θ1(t))n0zsin(0.5θ1(t))]T。
the method for performing quaternion operation fusion on the path planning results in all one-dimensional directions comprises the following steps:
calculating the rotation quaternion q (t) and the angular speed omega (t) after the synthesis at the current time t:
Figure BDA0002619311570000064
Figure BDA0002619311570000065
where [0, ω (t) ] is a pure four-element number consisting of a three-dimensional vector ω (t).
Compared with the prior art, the invention has the advantages and beneficial effects that:
1. the attitude maneuver planning under the condition that the angular velocities of the initial state and the target state of the satellite are not 0 can be realized, and the efficiency of the satellite for completing the maneuver task is improved.
2. Repeated iterative optimization is not needed, the calculation amount is small, the occupied satellite resources are small, and the method is easy to be applied practically.
3. The attitude maneuver planning can be carried out in real time, the problem of unstable numerical values does not exist, and the reliability is higher than that of the numerical value optimization method widely adopted at present.
Drawings
Fig. 1 is a flowchart of a method for planning a satellite attitude maneuver provided by the present invention.
FIG. 2 is a planning curve for satellite attitude in an embodiment of the present invention.
FIG. 3 is an error curve of the planning result with respect to the target pose in the embodiment of the present invention.
Fig. 4 is a planned curve of the angular velocity of the satellite in the embodiment of the present invention.
Fig. 5 is a planned curve of angular acceleration of a satellite in an embodiment of the invention.
Detailed Description
The preferred embodiment of the present invention will be described in detail below with reference to fig. 1 to 5.
As shown in fig. 1, the present invention provides a method for planning a satellite attitude maneuver, comprising the following steps:
and S1, decomposing the maneuver of the satellite on the three-dimensional space into a plurality of rotations in one-dimensional directions by using the relation between the quaternion and the three-dimensional rotation and the property of quaternion multiplication, and realizing the decoupling between the angular velocity maneuver and the angular maneuver.
And step S2, planning a maneuvering path with initial and final angular velocities not equal to zero by adopting an analytical method according to the rotation in each one-dimensional direction obtained after decomposition.
And step S3, performing quaternion operation fusion on the path planning results in all one-dimensional directions to obtain a final satellite attitude maneuver planning result.
In one embodiment of the invention, the most critical part of the invention is first performed, i.e. the three-dimensional rotation of the satellite is decomposed into one-dimensional rotations on a plurality of independent euler axes by decomposing the attitude quaternion.
Firstly, a satellite attitude kinematic model is given as follows:
Figure BDA0002619311570000071
the satellite attitude dynamics model is as follows:
Figure BDA0002619311570000072
wherein q is [ q ]0 q1 q2 q3]TAs quaternions of satellite attitude, ω ═ ωx ωy ωz]TAs the angular velocity of the attitude of the satellite,
Figure BDA0002619311570000073
is the attitude angular velocity in the form of pure four-element number, J is the rotational inertia matrix of the satellite, and h is the angular motion of the on-satellite rotating partAmount uc＝[ucx ucy ucz]TIn order to control the torque, the torque is controlled,
Figure BDA0002619311570000081
for quaternion multiplication, ω×Is a diagonally symmetric matrix of ω.
The input information used for the maneuver planning is: initial attitude quaternion qiTarget quaternion qfStarting time t of maneuveriEnd time tfDuration of maneuver Tm＝tf-tiThe angular velocity of the satellite at the start of the maneuver is ωi(in-system representation of satellite attitude), angular velocity ω after maneuvering into positionf(in-system representation of satellite attitude), upper limit of angular acceleration of maneuvering amax。
The problem of satellite attitude planning with non-zero initial and final angular velocities can be understood as given initial conditions (initial attitude quaternion q)i＝[qi0 qi1 qi2 qi3]TInitial angular velocity ωi＝[ωix ωiy ωiz]T) And terminal conditions (target attitude quaternion q)f＝[qf0 qf1 qf2 qf3]TTarget angular velocity ωf＝[ωfx ωfy ωfz]T) And solving the kinematic differential equation (1) by meeting the requirement of certain constraint conditions.
Assuming that the satellite always rotates around a specific rotation axis during the satellite maneuver, i.e. the angular velocity direction is constant in a coordinate system, it can be expressed as ω ═ ω | n, where | ω is the operation of solving the vector norm, and n ═ n [ n ]x ny nz]TTo represent the unit vector of the rotation axis, the satellite attitude at any time t during the maneuver can be represented as:
Figure BDA0002619311570000082
decomposing a target quaternion into q0、q1、q2Three rotational quaternions, here two rotational decomposition methods are used, which differ in the order in which the three rotational quaternions are multiplied. In an actual task, the rotation decomposition method is not limited to these two methods, and the number of rotations may be increased according to the constraint conditions of the task, and will not be described here.
The first rotational decomposition is:
Figure BDA0002619311570000083
wherein q is1To complete the rotational quaternion from the satellite attitude to the target attitude, q2Rotational quaternion, q, for satellite acceleration to target angular velocity0Then it is a rotational quaternion that eliminates the effect of the initial angular velocity.
The second rotational decomposition is:
Figure BDA0002619311570000084
wherein q is1To complete the rotational quaternion from the satellite attitude to the target attitude, q2Rotational quaternion, q, for acceleration of a satellite from an initial angular velocity to a target angular velocity0Is the rotational quaternion to calculate the initial angular velocity effect.
According to this first rotational decomposition method, at any time t e [ t ] in the course of the operationi,tf]The satellite-maneuvered instantaneous target quaternion q (t) is:
Figure BDA0002619311570000091
the instantaneous angular velocity of a satellite can be decomposed into:
Figure BDA0002619311570000092
according to the secondA rotary decomposition method, wherein t belongs to [ t ] at any time in the process of maneuveringi,tf]The satellite-maneuvered instantaneous target quaternion q (t) is:
Figure BDA0002619311570000093
the instantaneous angular velocity of a satellite can be decomposed into:
Figure BDA0002619311570000094
if the first rotary decomposition mode is adopted, q is planned0Initial angular velocity ωiTo 0. The rotation axis n of the rotation is obtained by the following formula0And any time t epsilon [ t ] in the maneuvering processi,tf]Instantaneous angular velocity ω of0(t) and quaternion q0(t)。
Figure BDA0002619311570000095
Figure BDA0002619311570000096
Figure BDA0002619311570000097
q0(t)＝[cos(0.5θ0(t))n0xsin(0.5θ0(t))n0ysin(0.5θ0(t))n0zsin(0.5θ0(t))]T (13)
If the second rotation mode is adopted, q is planned0Calculating the initial angular velocity omegaiThe influence of (c). The rotation axis n of the rotation is obtained by the following formula0And any time t epsilon [ t ] in the maneuvering processi,tf]Instantaneous angular velocity ω of0(t) and quaternion q0(t)。
Figure BDA0002619311570000101
ω0(t)＝ωi (15)
Figure BDA0002619311570000102
q0(t)＝[cos(0.5θ0(t))n0xsin(0.5θ0(t))n0ysin(0.5θ0(t))n0zsin(0.5θ0(t))]T (17)
If the first rotary decomposition mode is adopted, q is planned2Accelerating a satellite to omegaf. The rotation axis n of the rotation is obtained by the following formula2And any time t epsilon [ t ] in the maneuvering processi,tf]Instantaneous angular velocity ω of2(t) and quaternion q2(t)。
Figure BDA0002619311570000103
Figure BDA0002619311570000104
Figure BDA0002619311570000105
q2(t)＝[cos(0.5θ2(t))n0xsin(0.5θ2(t))n0ysin(0.5θ2(t))n0zsin(0.5θ2(t))]T (21)
If the second rotary decomposition mode is adopted, q is planned2The angular velocity of the satellite is changed from omegaiAccelerate to omegaf. First, ω is calculatediAnd ωfThe angular velocity difference between Δ ω.
Figure BDA0002619311570000106
Then according to delta omega to omega2(t) planning, i.e.
Figure BDA0002619311570000107
Figure BDA0002619311570000108
Figure BDA0002619311570000109
q2(t)＝[cos(0.5θ2(t))n0xsin(0.5θ2(t))n0ysin(0.5θ2(t))n0zsin(0.5θ2(t))]T (26)
By planning q1Taking satellite attitude from initial attitude qiRotate to target attitude qf. The rotation axis e of the rotation is obtained by the following formula1And any time t epsilon [ t ] in the maneuvering processi,tf]Instantaneous angular velocity ω of1(t) and quaternion q1(t)。
Figure BDA0002619311570000111
θ1(tf)＝2acos(q10) (28)
Figure BDA0002619311570000112
q1Acceleration/deceleration time t corresponding to rotationaccAnd a uniform time tconstComprises the following steps:
Figure BDA0002619311570000113
Figure BDA0002619311570000114
angular velocity omega1(t) is:
Figure BDA0002619311570000115
instantaneous angle of rotation theta1(t) is:
Figure BDA0002619311570000116
corresponding instantaneous quaternion q1(t) is:
q1(t)＝[cos(0.5θ1(t))n0xsin(0.5θ1(t))n0ysin(0.5θ1(t))n0zsin(0.5θ1(t))]T (34)
and calculating the rotation quaternion q (t) and the angular velocity omega (t) synthesized at the current moment t, namely the planned target quaternion and the planned angular velocity.
When the first rotary decomposition mode is adopted:
Figure BDA0002619311570000117
Figure BDA0002619311570000118
when the second rotary decomposition mode is adopted:
Figure BDA0002619311570000121
Figure BDA0002619311570000122
where [0, ω (t) ] is a pure four-element number consisting of a three-dimensional vector ω (t).
In order to improve the control precision in the maneuvering process, the angular acceleration corresponding to the planned angular velocity is obtained through a differential algorithm, and then the feedforward moment for the attitude tracking controller is calculated according to a satellite dynamics model. Let the next control instant adjacent to the current instant t be tnextThe planned angular acceleration a (t) at time t can be calculated according to the following formula
Figure BDA0002619311570000123
the feedforward moment of the satellite maneuver at time t is
Figure BDA0002619311570000124
Figure BDA0002619311570000125
The conditions for the mathematical simulation are as follows:
the rotational inertia of the satellite:
Figure BDA0002619311570000126
initial attitude quaternion of satellite:
qi＝[cos(π/8)sin(π/8)0 0]T
the corresponding rotational euler angles are:
Figure BDA0002619311570000127
θ＝ψ＝0°
initial angular velocity:
ωi＝[-0.1 0.2 -0.1]T(°/s)
satellite target attitude quaternion:
qf＝[cos(π/8)0 sin(π/8)0]T
the corresponding rotational euler angles are:
θ＝45°，
Figure BDA0002619311570000128
target angular velocity:
ωf＝[0.1 -0.2 0.1]T(°/s)
constraint conditions are as follows: the maximum angular velocity of the three axes is less than 0.8 degree/s, and the angular acceleration is less than 0.4 degree/s2。
The mathematical simulation results are shown in fig. 2 to 5, and fig. 2 is an attitude euler angle obtained by a planned attitude quaternion according to a yaw-roll-pitch rotation sequence. Compared with quaternions, the result of the Euler angle can more intuitively show the satellite attitude change in the maneuvering process. Fig. 3 is the error between the satellite planning attitude and the final target attitude during the whole maneuver, which converges to 0 at the end of the maneuver, indicating that the planning result satisfies the constraint of the target attitude. Fig. 4 shows the planned angular velocity, and both the initial value and the terminal value satisfy the requirements of the initial and final constraints of the planning. Fig. 5 is a planned angular acceleration.
Compared with the prior art, the invention has the advantages and beneficial effects that:
1. the attitude maneuver planning under the condition that the angular velocities of the initial state and the target state of the satellite are not 0 can be realized, and the efficiency of the satellite for completing the maneuver task is improved.
2. Repeated iterative optimization is not needed, the calculation amount is small, the occupied satellite resources are small, and the method is easy to be applied practically.
3. The attitude maneuver planning can be carried out in real time, the problem of unstable numerical values does not exist, and the reliability is higher than that of the numerical value optimization method widely adopted at present.
While the present invention has been described in detail with reference to the preferred embodiments, it should be understood that the above description should not be taken as limiting the invention. Various modifications and alterations to this invention will become apparent to those skilled in the art upon reading the foregoing description. Accordingly, the scope of the invention should be determined from the following claims.

Claims (2)

1. A satellite attitude maneuver planning method is characterized in that the maneuver of a satellite in a three-dimensional space is decomposed into a plurality of rotations in one-dimensional directions by utilizing the relation between quaternions and three-dimensional rotations and the property of quaternion multiplication, a maneuver path with the initial and final angular velocities not being zero is planned by adopting an analytic method aiming at the rotation in each one-dimensional direction obtained after decomposition, and quaternion operation fusion is carried out on path planning results in all one-dimensional directions to obtain a final satellite attitude maneuver planning result;
the method for decomposing the maneuvering of the satellite on the three-dimensional space into the rotations in a plurality of one-dimensional directions comprises the following steps: target quaternion q for attitude maneuverfDecomposition into q0、q1、q2Three rotational quaternions;
Figure FDA0003394856180000011
wherein,
Figure FDA0003394856180000012
for quaternion multiplication, q1To complete the rotational quaternion from the satellite attitude to the target attitude, q2Rotational quaternion, q, for satellite acceleration to target angular velocity0Is a rotational quaternion to eliminate the effect of the initial angular velocity;
at any time t e [ t ] in the maneuvering processi,tf]The satellite-maneuvered instantaneous target quaternion q (t) is:
Figure FDA0003394856180000013
the instantaneous angular velocity of a satellite is decomposed into:
Figure FDA0003394856180000014
the method for planning the maneuvering path with the initial angular velocity and the final angular velocity not equal to zero comprises the following steps:
by planning q0Initial angular velocity ωiLowered to 0, and the rotational axis n of the rotation is obtained0And any time t epsilon [ t ] in the maneuvering processi,tf]Instantaneous angular velocity ω of0(t) and quaternion q0(t)；
Figure FDA0003394856180000015
Figure FDA0003394856180000016
Figure FDA0003394856180000017
q0(t)＝[cos(0.5θ0(t)) n0xsin(0.5θ0(t)) n0ysin(0.5θ0(t)) n0zsin(0.5θ0(t))]T
By planning q2Accelerating a satellite to an angular velocity ωfDetermining the rotation axis n of the rotation2And any time t epsilon [ t ] in the maneuvering processi,tf]Instantaneous angular velocity ω of2(t) and quaternion q2(t)；
Figure FDA0003394856180000021
Figure FDA0003394856180000022
Figure FDA0003394856180000023
q2(t)＝[cos(0.5θ2(t)) n0xsin(0.5θ2(t)) n0ysin(0.5θ2(t)) n0zsin(0.5θ2(t))]T；
By planning q1Taking satellite attitude from initial attitude qiRotate to target attitude qfDetermining the rotation axis n of the rotation1And any time t epsilon [ t ] in the maneuvering processi,tf]Instantaneous angular velocity ω of1(t) and quaternion q1(t)；
Figure FDA0003394856180000024
θ1(tf)＝2a cos(q10)
Figure FDA0003394856180000025
q1Acceleration/deceleration time t corresponding to rotationaccAnd a uniform time tconstComprises the following steps:
Figure FDA0003394856180000026
Figure FDA0003394856180000027
angular velocity omega1(t) is:
Figure FDA0003394856180000028
instantaneous angle of rotation theta1(t) is:
Figure FDA0003394856180000029
corresponding instantaneous quaternion q1(t) is:
q1(t)＝[cos(0.5θ1(t)) n0xsin(0.5θ1(t)) n0ysin(0.5θ1(t)) n0zsin(0.5θ1(t))]T
the method for performing quaternion operation fusion on the path planning results in all one-dimensional directions comprises the following steps:
calculating the rotation quaternion q (t) and the angular speed after the synthesis at the current time t:
Figure FDA0003394856180000031
Figure FDA0003394856180000032
where [0, ω (t) ] is a pure four-element number consisting of a three-dimensional vector ω (t).
2. A satellite attitude maneuver planning method is characterized in that the maneuver of a satellite in a three-dimensional space is decomposed into a plurality of rotations in one-dimensional directions by utilizing the relation between quaternions and three-dimensional rotations and the property of quaternion multiplication, a maneuver path with the initial and final angular velocities not being zero is planned by adopting an analytic method aiming at the rotation in each one-dimensional direction obtained after decomposition, and quaternion operation fusion is carried out on path planning results in all one-dimensional directions to obtain a final satellite attitude maneuver planning result;
the satellite is in the space of three dimensionsThe method for resolving the maneuvering in the room into the rotations in the plurality of one-dimensional directions comprises the following steps: target quaternion q for attitude maneuverfDecomposition into q0、q1、q2Three rotational quaternions;
Figure FDA0003394856180000033
wherein,
Figure FDA0003394856180000034
for quaternion multiplication, q1To complete the rotational quaternion from the satellite attitude to the target attitude, q2Rotational quaternion, q, for acceleration of a satellite from an initial angular velocity to a target angular velocity0Is a rotational quaternion to calculate the effect of the initial angular velocity;
at any time t e [ t ] in the maneuvering processi,tf]The satellite-maneuvered instantaneous target quaternion q (t) is:
Figure FDA0003394856180000035
the instantaneous angular velocity of a satellite is decomposed into:
Figure FDA0003394856180000041
the method for planning the maneuvering path with the initial angular velocity and the final angular velocity not equal to zero comprises the following steps:
by planning q0Calculating the initial angular velocity omegaiTo find the axis of rotation n of the rotation0And any time t epsilon [ t ] in the maneuvering processi,tf]Instantaneous angular velocity ω of0(t) and quaternion q0(t)；
Figure FDA0003394856180000042
ω0(t)＝ωi
Figure FDA0003394856180000043
q0(t)＝[cos(0.5θ0(t)) n0xsin(0.5θ0(t)) n0ysin(0.5θ0(t)) n0zsin(0.5θ0(t))]T
By planning q2The angular velocity of the satellite is changed from omegaiAccelerate to omegafCalculate ωiAnd ωfThe angular velocity difference Δ ω therebetween;
Figure FDA0003394856180000044
from Δ ω to ω2(t) planning;
Figure FDA0003394856180000045
Figure FDA0003394856180000046
Figure FDA0003394856180000047
q2(t)＝[cos(0.5θ2(t)) n0xsin(0.5θ2(t)) n0ysin(0.5θ2(t)) n0zsin(0.5θ2(t))]T
by planning q1Taking satellite attitude from initial attitude qiRotate to target attitude qfDetermining the rotation axis n of the rotation1And any time t epsilon [ t ] in the maneuvering processi,tf]In the momentAngular velocity ω1(t) and quaternion q1(t)；
Figure FDA0003394856180000048
θ1(tf)＝2a cos(q10)
Figure FDA0003394856180000051
q1Acceleration/deceleration time t corresponding to rotationaccAnd a uniform time tconstComprises the following steps:
Figure FDA0003394856180000052
Figure FDA0003394856180000053
angular velocity omega1(t) is:
Figure FDA0003394856180000054
instantaneous angle of rotation theta1(t) is:
Figure FDA0003394856180000055
corresponding instantaneous quaternion q1(t) is:
q1(t)＝[cos(0.5θ1(t)) n0xsin(0.5θ1(t)) n0ysin(0.5θ1(t)) n0zsin(0.5θ1(t))]T
the method for performing quaternion operation fusion on the path planning results in all one-dimensional directions comprises the following steps:
calculating the rotation quaternion q (t) and the angular speed omega (t) after the synthesis at the current time t:
Figure FDA0003394856180000056
Figure FDA0003394856180000057
where [0, ω (t) ] is a pure four-element number consisting of a three-dimensional vector ω (t).
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CN106945849A (en) * 2017-03-30 2017-07-14 上海航天控制技术研究所 A kind of motor-driven method of attitude of satellite based on Discrete control
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