CN110262537B - Multi-constraint spacecraft fast attitude maneuver parameterization deterministic planning method - Google Patents

Multi-constraint spacecraft fast attitude maneuver parameterization deterministic planning method Download PDF

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CN110262537B
CN110262537B CN201910571614.8A CN201910571614A CN110262537B CN 110262537 B CN110262537 B CN 110262537B CN 201910571614 A CN201910571614 A CN 201910571614A CN 110262537 B CN110262537 B CN 110262537B
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attitude
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path
pointing
angular velocity
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CN110262537A (en
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徐瑞
王辉
崔平远
朱圣英
梁子璇
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Beijing Institute of Technology BIT
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
    • G05D1/00—Control of position, course or altitude of land, water, air, or space vehicles, e.g. automatic pilot
    • G05D1/08—Control of attitude, i.e. control of roll, pitch, or yaw
    • G05D1/0808—Control of attitude, i.e. control of roll, pitch, or yaw specially adapted for aircraft
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
    • G05D1/00—Control of position, course or altitude of land, water, air, or space vehicles, e.g. automatic pilot
    • G05D1/10—Simultaneous control of position or course in three dimensions
    • G05D1/101—Simultaneous control of position or course in three dimensions specially adapted for aircraft

Abstract

The invention relates to a parameterization deterministic planning method for rapid attitude maneuver of a spacecraft under multiple constraints, belonging to the technical field of spacecraft attitude planning. The method determines the current initial rotation matrix and angular velocity of the attitude maneuver, and the target rotation matrix and angular velocity to obtain the attitude path on the virtual domain. And detecting to obtain an area violating the pointing constraint on the current section attitude path. And for each block of pointing constraint violation area, generating segmentation nodes in the middle position of the pointing constraint violation area, and then sequentially solving to obtain each segment of attitude path. And aiming at the obtained attitude path on the virtual domain meeting the pointing constraint, obtaining the quick attitude maneuver trajectory, the angular velocity and the control moment on the time domain meeting the bounded constraint and the dynamic constraint by using a time optimal path parameterization method, namely obtaining the quick attitude maneuver trajectory, the angular velocity and the control moment on the time domain meeting various constraints finally. The invention has no randomness, stable result and more reliable actual satellite application.

Description

Multi-constraint spacecraft fast attitude maneuver parameterization deterministic planning method
Technical Field
The invention relates to a parameterization deterministic planning method for rapid attitude maneuver of a spacecraft under multiple constraints, belonging to the technical field of spacecraft attitude planning.
Background
Spacecraft often need the ability to have fast attitude maneuvers while performing specific space tasks. For example, earth observation satellites require fast attitude maneuvers to increase the effectiveness of the task and image acquisition capabilities. Meanwhile, in order to prevent the optical sensors such as the star sensor from being damaged, the optical sensors on the spacecraft need to avoid direct irradiation of bright celestial bodies such as the sun in the attitude maneuver process, and therefore the pointing constraint in the attitude maneuver process is formed. In addition, actuators on spacecraft generally provide only limited control torque; the gyroscope, the sun sensor and other instruments on the spacecraft need the angular velocity of the spacecraft not to be too high, otherwise, poor angular velocity measurement and attitude estimation results can be caused; this forms a bounded constraint on the control moment and angular velocity during the attitude maneuver. And finally, the attitude kinematics and the dynamic constraint of the spacecraft need to be satisfied in the attitude maneuver process.
The initial research only aims at the problem of feasible solution of constrained attitude maneuver planning, and the main methods include a potential function method, a random planning algorithm, a semi-definite planning method and the like. The attitude maneuver under the feasible solution can not optimize the attitude maneuver process, and can not meet the requirement of the quick attitude maneuver task on maneuver time. The problem of attitude maneuver planning has been difficult to solve given the many complex constraints. And optimization indexes are introduced, and the problem solving work becomes a huge challenge. Aiming at the problem of time optimal constraint attitude maneuver planning, Nguyen and the like adopt a three-step solution idea, firstly, an attitude path meeting pointing constraint on a virtual domain is planned based on a fast search random tree method, then, a maneuver track meeting bounded constraint and dynamic constraint is obtained by aiming at the obtained path through a time optimal path parameterization method, and finally, the maneuver time of the obtained maneuver track is reduced through continuous iterative optimization.
The existing method on the virtual domain can obtain a short-time attitude maneuver trajectory quickly under the average condition, but the method has randomness, and the calculation efficiency and the planning result of the method have great fluctuation. In the practical on-satellite application, on one hand, the attitude maneuver planning result can be obtained only after a long time in a single solving process, the quick response and execution of the practical attitude maneuver process are delayed, and even the execution time is missed; on the other hand, the attitude maneuver time which can be obtained in a single solving process is long, and the quick attitude maneuver cannot be realized; in conclusion, the method is unreliable in practical satellite application, and has various hidden dangers in the process of quick attitude maneuver.
Disclosure of Invention
The invention aims to solve the problem that the existing method has randomness, so that the hidden dangers such as quick response delay and the like exist in the process of quick attitude maneuver of a spacecraft, and provides a parameterization deterministic planning method for the quick attitude maneuver of the spacecraft under multiple constraints. The method adopts a deterministic attitude path planning method on a virtual domain and is combined with a time optimal path parameterization method to obtain a quick multi-constraint attitude maneuver track, an angular speed and a control moment, the solving speed is high, the randomness is avoided, the result is stable, and the actual on-satellite application is more reliable.
The purpose of the invention is realized by the following technical scheme.
The invention discloses a parameterization deterministic planning method for rapid attitude maneuver of a spacecraft under multiple constraints, which is used for determining a current initial rotation matrix and angular speed of the attitude maneuver, and a target rotation matrix and angular speed to obtain an attitude path on a virtual domain. And detecting to obtain an area violating the pointing constraint on the current section attitude path. And for each block of pointing constraint violation area, generating segmentation nodes in the middle position of the pointing constraint violation area, and then sequentially solving to obtain each segment of attitude path. And aiming at the obtained attitude path on the virtual domain meeting the pointing constraint, obtaining the quick attitude maneuver trajectory, the angular velocity and the control moment on the time domain meeting the bounded constraint and the dynamic constraint by using a time optimal path parameterization method, namely obtaining the quick attitude maneuver trajectory, the angular velocity and the control moment on the time domain meeting various constraints finally.
The invention discloses a parameterization deterministic planning method for rapid attitude maneuver of a spacecraft under multiple constraints, which comprises the following implementation steps:
step one, determining the current initial rotation matrix of the attitude maneuver
Figure BDA0002111027940000021
And angular velocity ω0And a target rotation matrix
Figure BDA0002111027940000022
And angular velocity ω1To obtain a virtual domain p ∈ [0,1 ]]Upper posture path
Figure BDA0002111027940000023
Figure BDA0002111027940000024
In the formula (I), the compound is shown in the specification,<x>is represented by the vector x ═ x1,x2,x3]TThe defined oblique symmetry matrix is shown in formula (2). e.g. of the type<x>The matrix index of the diagonally symmetric matrix generated by the vector x is expressed as shown in equation (3). And | x | represents solving the 2 norm of the vector x. I is3Identity matrix representing 3 × 3. coefficient vector
Figure BDA0002111027940000025
And
Figure BDA0002111027940000026
obtained by solving a system of equations (4) in which the vectors are
Figure BDA0002111027940000027
And satisfy
Figure BDA0002111027940000028
H (x) represents the matrix generated by vector x, as shown in equation (5).
Figure BDA0002111027940000029
Figure BDA0002111027940000031
Figure BDA0002111027940000032
Figure BDA0002111027940000033
Step two, detecting and obtaining the current section attitude path obtained in the step one through a formula (6)
Figure BDA0002111027940000034
The number of the regions violating the pointing constraint and the number of the regions violating the pointing constraint are N. For each block of the pointing constraint violation area, a segmentation node is generated at a position intermediate to the pointing constraint violation area. And N segmented nodes are obtained in total, and then the N +1 segments of attitude paths are obtained by sequentially solving. Each segment beingIf the orientation constraint is violated again in the solving process of the gesture path, the gesture path needs to be segmented again. The specific steps are divided into 2.1 to 2.5.
2.1, judging whether the current section attitude path obtained in the step one violates the pointing constraint or not through a formula (6); if not, executing the step three; yes, perform 2.2;
2.2, for each block of the pointing constraint violation area, generating a segmented node at the middle position of the pointing constraint violation area;
2.3, calculating the attitude path of the section according to the formulas (1) to (5); judging whether the gesture path of the segment violates the pointing constraint; if not, executing 2.4; is, repeat 2.2 to 2.5;
2.4, calculating the next section of attitude path through formulas (1) to (5);
2.5, judging whether the next section of posture path has contra-directional constraint; if not, repeating 2.4 to 2.5 until all N +1 sections of attitude paths are solved, and executing the step three; is, repeat 2.2 to 2.5.
Attitude CIBViolating the directional constraint is expressed in the form:
Figure BDA0002111027940000035
in the formula (I), the compound is shown in the specification,
Figure BDA0002111027940000036
representing the component of the unit direction vector of the spacecraft to the bright celestial body in the inertial frame.
Figure BDA0002111027940000037
And the unit direction vector of the sensor under the body coordinate system is shown. Theta is the orientation constraint angle. n represents the number of pointing constraints.
And step three, aiming at the attitude path on the virtual domain which meets the pointing constraint and is obtained in the steps from the step one to the step two, obtaining the fast attitude maneuver track, the angular velocity and the control moment on the time domain which meet the bounded constraint and the dynamic constraint by using a time optimal path parameterization method.
The control moment and angular velocity bounded constraint equations are as follows:
|ui|≤umax,i＝1,2,3 (7)
|ωi|≤ωmax,i＝1,2,3 (8)
wherein u is [ u ]1,u2,u3]TThe control moment in the body coordinate system is shown. Omega ═ omega1,ω2,ω3]TRepresenting the angular velocity of the spacecraft in a body coordinate system.
The attitude dynamics constraint equation is as follows:
Figure BDA0002111027940000041
where J represents the inertia matrix of the spacecraft × represents the vector cross product.
And step four, outputting the final quick attitude maneuver trajectory, the angular speed and the control moment on the time domain which meet various constraints.
Has the advantages that:
the invention discloses a parameterization deterministic planning method for spacecraft fast attitude maneuver under multiple constraints, which adopts a deterministic attitude path planning method on a virtual domain and a time optimal path parameterization method to obtain fast attitude maneuver tracks, angular speeds and control moments on a time domain which meet multiple complex constraints such as pointing constraint, bounded constraint, dynamics constraint and the like, and has the advantages of high solving speed, no randomness, stable result and more reliable actual on-satellite application.
Drawings
FIG. 1 is a flow chart of a parameterization deterministic planning method for fast attitude maneuver of a spacecraft under multiple constraints according to the invention;
FIG. 2 is a two-dimensional longitude and latitude diagram of a maneuvering track of a view axis of the star sensor under an inertial coordinate system;
FIG. 3 is a graph of angular velocity during an attitude maneuver;
fig. 4 is a control torque variation curve during the attitude maneuver.
Detailed Description
The invention is further explained below with reference to the figures and examples.
Example 1
As shown in fig. 1, the method for parameterization deterministic planning of fast attitude maneuver of spacecraft under multiple constraints disclosed in this embodiment specifically includes the following steps:
in this embodiment, the spacecraft needs to perform a large-angle fast attitude maneuver in order to perform the earth observation task. The starting and target conditions of the gesture maneuvers are shown in equation (10). And 1 star sensor is arranged in the positive direction of the Z axis of the spacecraft. In order to prevent the star sensor from being damaged, the view field of the star sensor needs to avoid bright celestial bodies such as the sun and the moon in the attitude maneuver process. The spacecraft adopts a control moment gyroscope as an actuating mechanism, and the maximum moment which can be provided is 17 N.m. The maximum angular velocity allowed for the spacecraft is 2.8 deg/s.
Step one, determining the current initial rotation matrix of the attitude maneuver
Figure BDA0002111027940000051
And angular velocity ω0And a target rotation matrix
Figure BDA0002111027940000052
And angular velocity ω1To obtain a virtual domain p ∈ [0,1 ]]Upper posture path
Figure BDA0002111027940000053
Figure BDA0002111027940000054
In this embodiment, the starting rotation matrix of the spacecraft attitude maneuver
Figure BDA0002111027940000055
And angular velocity ωsAnd a target rotation matrix
Figure BDA0002111027940000056
And angular velocity ωgAs shown in equation (10). First determined current start spinThe rotation matrix and angular velocity and the target rotation matrix and angular velocity are the same as the total starting and target boundary conditions of the attitude maneuver, i.e.
Figure BDA0002111027940000057
ω0＝ωs、
Figure BDA0002111027940000058
And ω1＝ωg. And determining the current initial and target rotation matrixes in the solving process from the segmented nodes obtained in the step two. The current starting and target angular velocities corresponding to the segmentation nodes are non-zero angular velocities close to zero, i.e. ω0＝[0.01ωmax,0.01ωmax,0.01ωmax]TOr ω1＝[0.01ωmax,0.01ωmax,0.01ωmax]T. In this embodiment, the first current segment attitude path is obtained by using equations (1) to (5)
Figure BDA00021110279400000510
Wherein h is [5.780943, -0.307095,1.470419]T、k＝[-8.671415,0.460642,-2.205629]TAnd l ═ 0,0]T。
Step two, detecting and obtaining the current section attitude path obtained in the step one through a formula (6)
Figure BDA0002111027940000059
The number of the regions violating the pointing constraint and the number of the regions violating the pointing constraint are N. For each block of the pointing constraint violation area, a segmentation node is generated at a position intermediate to the pointing constraint violation area. And N segmented nodes are obtained in total, and then the N +1 segments of attitude paths are obtained by sequentially solving. Each pose path needs to be segmented again if the orientation constraint is violated again during the solution process.
TABLE 1 Direction constraint parameters
Figure BDA0002111027940000061
TABLE 2 attitude path coefficient vector
Figure BDA0002111027940000062
In this embodiment, the spacecraft is provided with 1 star sensor in the positive Z-axis direction, namely rB,1＝rB,2＝[0,0,1]T. In the process of attitude maneuver, the star sensor needs to avoid 2 bright celestial bodies, namely n is 2. The pointing constraint parameters are shown in table 1. In this embodiment, the current segment pose path obtained in step one
Figure BDA0002111027940000063
And (4) sequentially solving to obtain 2 sections of attitude paths when the number N of the upward pointing constraint violation areas is equal to 1. If the 1 st section of attitude path violates the pointing constraint again and the number of the regions violated by the pointing constraint is 1, the 1 st section of attitude path needs to be divided into 2 small sections of attitude paths again for solving; these 2 small segments of the pose path then all satisfy the pointing constraints. The 2 nd pose path also directly satisfies the pointing constraint. Therefore, a total of 3 pose paths are finally solved, as shown in table 2.
And step three, aiming at the attitude path on the virtual domain which meets the pointing constraint and is obtained in the steps from the step one to the step two, obtaining the fast attitude maneuver track, the angular velocity and the control moment on the time domain which meet the bounded constraint and the dynamic constraint by using a time optimal path parameterization method.
TABLE 3 inertia matrix and control moments and angular velocities of spacecraft bounded constraints
Figure BDA0002111027940000064
In this embodiment, the inertia matrix of the spacecraft and the control moments and angular velocities are bounded as shown in Table 3. The 3 sections of attitude paths obtained from the step one to the step two are uniformly expressed as
Figure BDA0002111027940000071
Wherein c (p) ═ p3h+p2k + pl is the piecewise vector function as shown in table 2. Utilizing time-optimal path parametersThe digitalization method is used for the existing path c (p) (p ∈ [0,3 ]]) Performing temporal parameterization p (T) (T ∈ [0, T)]) The obtained angular velocity and the control torque are shown in equations (11) and (12), respectively. And then, solving the optimal p and the corresponding relation p (t) of the time domain and the virtual domain by using a time optimal path parameterization method, and further obtaining the fast attitude maneuver trajectory, the angular velocity and the control moment on the time domain which meet the bounded constraint and the dynamic constraint. In this embodiment, the solved optimal attitude maneuver time T is 61.81 s.
Figure BDA0002111027940000072
Figure BDA0002111027940000073
Wherein c is a shorthand notation for c (p).
Figure BDA0002111027940000074
Is the first derivative of c with respect to the parameter p.
Figure BDA0002111027940000075
Is the second derivative of c on the parameter p. g (c, c)p) Is formed by c and cpThe resulting vector is shown in equation (13).
Figure BDA0002111027940000076
And step four, outputting the final fast attitude maneuver trajectory, the angular speed and the control moment on the time domain which meet various constraints, wherein the fast attitude maneuver trajectory, the angular speed and the control moment are respectively shown in the figure 2, the figure 3 and the figure 4.
The method runs on an ordinary PC, the average running time is 0.27s, the solving speed is high, the change of the running time is small, and the maneuvering time of the gesture planned each time is the same. The direct euler rotation angle of the present embodiment from the start rotation matrix to the target rotation matrix is 171.12 degrees. For such a large-angle attitude maneuver, the attitude maneuver time obtained in this embodiment is 61.81s, which is a very fast attitude maneuver result. As can be seen from fig. 2, 3 and 4, the gesture maneuver trajectory can safely avoid multiple pointing constraints, and both the angular velocity and the control torque satisfy the corresponding bounded constraints.
The embodiment shows that the method adopts a deterministic attitude path planning method on the virtual domain and is combined with a time optimal path parameterization method to obtain the fast attitude maneuver trajectory, the angular velocity and the control moment on the time domain which meet various complex constraints such as pointing constraint, bounded constraint, dynamics constraint and the like, the solving speed is fast, the randomness is avoided, the result is stable, and the actual on-satellite application is more reliable.
The above detailed description is intended to illustrate the objects, aspects and advantages of the present invention, and it should be understood that the above detailed description is only exemplary of the present invention and is not intended to limit the scope of the present invention, and any modifications, equivalents, improvements and the like within the spirit and principle of the present invention should be included in the scope of the present invention.

Claims (1)

1. The method for parameterizing and deterministically planning the rapid attitude maneuver of the spacecraft under multiple constraints is characterized by comprising the following steps: the method comprises the following implementation steps:
step one, determining the current initial rotation matrix of the attitude maneuver
Figure FDA0002413095270000011
And angular velocity ω0And a target rotation matrix
Figure FDA0002413095270000012
And angular velocity ω1To obtain a virtual domain p ∈ [0,1 ]]Upper posture path
Figure FDA0002413095270000013
Figure FDA0002413095270000014
In the formula (I), the compound is shown in the specification,<x>is represented by the vector x ═ x1，x2，x3]TA defined oblique symmetry matrix, as shown in formula (2); e.g. of the type<x>A matrix index representing the diagonally symmetric matrix generated by the vector x, as shown in equation (3); the | x | represents solving the 2 norm of the vector x; i is3Identity matrix representing 3 × 3, coefficient vector
Figure FDA0002413095270000015
And
Figure FDA0002413095270000016
obtained by solving a system of equations (4) in which the vectors are
Figure FDA0002413095270000017
And satisfy
Figure FDA0002413095270000018
H (x) represents the matrix generated by vector x, as shown in equation (5);
Figure FDA0002413095270000019
Figure FDA00024130952700000110
Figure FDA00024130952700000111
Figure FDA00024130952700000112
step two, detecting and obtaining the current section attitude path obtained in the step one through a formula (6)
Figure FDA00024130952700000113
Region with upper violation of pointing constraint and pointing constraintThe number N of beam violation areas; for each block of the pointing constraint violation area, generating a segmented node at the middle position of the pointing constraint violation area; n segmented nodes are calculated, and then N +1 segments of attitude paths are obtained through solving in sequence; if the orientation constraint is violated again in the solving process of each section of attitude path, the section is needed to be segmented again; the specific steps are 2.1 to 2.5;
2.1, judging whether the current section attitude path obtained in the step one violates the pointing constraint or not through a formula (6); if not, executing the step three; yes, perform 2.2;
2.2, for each block of the pointing constraint violation area, generating a segmented node at the middle position of the pointing constraint violation area;
2.3, calculating the attitude path of the section according to the formulas (1) to (5); judging whether the gesture path of the segment violates the pointing constraint; if not, executing 2.4; is, perform 2.2 to 2.5;
2.4, calculating the next section of attitude path through formulas (1) to (5);
2.5, judging whether the next section of posture path has contra-directional constraint; if not, repeating 2.4 to 2.5 until all N +1 sections of attitude paths are solved, and executing the step three; is, repeat 2.2 to 2.5;
attitude CIBViolating the directional constraint is expressed in the form:
Figure FDA0002413095270000021
in the formula (I), the compound is shown in the specification,
Figure FDA0002413095270000022
representing the component of a unit direction vector of the spacecraft to the bright celestial body under an inertial coordinate system;
Figure FDA0002413095270000023
representing a unit direction vector of the sensor under a body coordinate system; theta is an orientation constraint angle; n represents the number of pointing constraints;
step three, aiming at the attitude path on the virtual domain which meets the pointing constraint and is obtained in the step one to the step two, a time optimal path parameterization method is utilized to obtain a fast attitude maneuver track, an angular velocity and a control moment on the time domain which meet the bounded constraint and the dynamic constraint;
the control moment and angular velocity bounded constraint equations are as follows:
|ui|≤umax，i＝1，2，3 (7)
|ωi|≤ωmax，i＝1，2，3 (8)
wherein u is [ u ]1，u2，u3]TRepresenting the control moment under a body coordinate system; omega ═ omega1，ω2，ω3]TRepresenting the angular velocity of the spacecraft in a body coordinate system;
the attitude dynamics constraint equation is as follows:
Figure FDA0002413095270000024
wherein J represents the inertia matrix of the spacecraft, × represents the vector cross product;
and step four, outputting the final quick attitude maneuver trajectory, the angular speed and the control moment on the time domain which meet various constraints.
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