A method for calculating a desired attitude trajectory of a satellite when observing a space object

Abstract

The application discloses a kind of expected attitude trajectory calculation methods when satellite observes space target, comprising the following steps: step S1, the inertial vector of satellite pointing target and its representation in orbit coordinate system are calculated;Step S2, the expected attitude of other two axes except optical axis direction is calculated using optical axis pointing constraint;Step S3, the expected attitude of optical axis direction is calculated using field of view constraint.The application is applicable to the case that there is requirement to camera field of view in target observation process, and the expected attitude under specific field of view constraint can be known.

Description

Technical Field

[0001] This invention relates to the field of satellite attitude control technology, and in particular to a method for calculating the desired attitude trajectory of a satellite when observing a space target. Background Technology

[0002] Under certain mission requirements, satellites utilize their onboard payloads, such as cameras and radar, to stare, track, and push-broom space targets or regions. Therefore, the satellite platform must adjust its attitude to ensure the precise pointing of a specific payload axis toward the target, thus providing the payload with the necessary attitude for operation. When the onboard payload is a square wide-field-of-view camera, and there are field-of-view constraints when observing the target area, simply calculating the optical axis attitude by eliminating phase rotation may not meet the field-of-view requirements during observation. Therefore, calculations must be performed based on the specific constraints of the field of view. Summary of the Invention

[0003] The purpose of this invention is to provide a method for calculating the desired attitude trajectory when a satellite observes a space target. This method is applicable to situations where there are requirements for the camera's field of view during target observation and can determine the desired attitude under specific field of view constraints.

[0004] To achieve the above objectives, the present invention is implemented through the following technical solution:

[0005] A method for calculating the desired attitude trajectory of a satellite when observing a space target, characterized by the following steps:

[0006] Step S1: Calculate the inertial vector of the satellite pointing towards the target and its representation in the orbital coordinate system;

[0007] Step S2: Calculate the desired attitude of the two axes other than the optical axis direction using the optical axis pointing constraint;

[0008] Step S3: Calculate the desired attitude along the optical axis using field-of-view constraints.

[0009] Step S1 specifically includes:

[0010] Step S1.1: Calculate the satellite's vector coordinates in the orbital system;

[0011] The satellite's vector r pointing towards the Earth's center s In a satellite orbital system, it is represented as

[0012]

[0013] Here, the superscript 'o' indicates the description of the vector in the orbital frame, R s The orbital radius is calculated using the following formula:

[0014]

[0015] Where a, e, and f are the semi-major axis, eccentricity, and true anomaly angle of the satellite orbit, respectively. Considering the small eccentricity, the orbital radius R can be assumed to be... s If the changes are small, then the velocity and acceleration vectors in the orbital frame are:

[0016]

[0017] Step S1.2: Calculate the target's vector coordinates in the inertial frame;

[0018] Assume the target's vector coordinates r t Given that the representation in an inertial frame is denoted as r t i The superscript 'i' indicates the vector description in the inertial frame, and the corresponding velocity and acceleration vectors in the inertial frame are denoted as . and

[0019] Step S1.3: Calculate the inertial vector of the satellite pointing towards the target and its representation in the orbital coordinate system;

[0020] Based on the positional relationship between the satellite and the target, the vector l pointing from the satellite to the target can be represented in the orbital system as follows:

[0021]

[0022] Among them, A oi The transformation matrix from the inertial frame to the orbital frame.

[0023]

[0024] Where u, i, and Ω are the latitudinal argument, inclination, and right ascension of the ascending node of the satellite orbit, respectively;

[0025] For l o Differentiating gives

[0026]

[0027]

[0028] Where, ω oi =[0 -|ω0| 0] T Let ω0 be the projection of the angular velocity of the orbital frame relative to the inertial frame onto the orbital frame, where ω0 is the orbital angular velocity. For ω oi antisymmetric matrix

[0029]

[0030] The vector l pointing from the satellite to the target is represented in the inertial frame as:

[0031]

[0032] Differentiating with respect to time has

[0033]

[0034] Step S2 specifically includes:

[0035] Step S2.1, calculate l o unit vector ρ o and its first and second derivatives;

[0036]

[0037]

[0038]

[0039] Step S2.2: Calculate the attitude angles, angular velocities, and angular accelerations of the roll axis and yaw axis;

[0040] According to the pointing constraint, the camera optical axis should be parallel to the target vector l during the imaging process. Assume that the camera optical axis points to the body + Y. b If the direction is such that the unit vector of the optical axis in this system is ρ, then... b =[0 1 0] T The superscript 'b' indicates the vector description in this system. Using Euler angles 312 transformation order to describe the satellite attitude, ρ can be obtained. b and relation

[0041]

[0042] Among them, A ob The attitude transformation matrix from the local system to the orbital system under the 312 transformation sequence is given by A. bo The transpose is obtained

[0043]

[0044] Then the attitude roll angle and yaw angle described in the orbital frame can be calculated.

[0045]

[0046]

[0047] Differentiating the above equation with respect to time yields the corresponding roll and yaw Euler angular velocities and angular accelerations:

[0048]

[0049]

[0050]

[0051]

[0052] According to the kinematic equations, the angular velocities of the roll and yaw directions relative to the orbital system are:

[0053]

[0054] Step S3 specifically includes:

[0055] Step S3.1: Determine the camera's field of view constraints;

[0056] When the optical axis points to the target, it can also rotate around itself. Therefore, other constraints are needed to determine the satellite's third attitude, namely its pitch attitude. To facilitate image stitching, the camera must always remain upright relative to the equatorial plane when taking pictures. That is, the horizontal central axis of the camera's field of view must be parallel to the equatorial plane. Therefore, the camera's field of view constraint can be understood as the roll axis OX. b It should be parallel to the inertial frame X. i O i Y i The plane, which is the inertial attitude pitch angle θ bi =0, and thus the pitch angular velocity and angular acceleration can be obtained.

[0057] Step S3.2, calculate l i unit vector ρ i and its first and second derivatives;

[0058]

[0059]

[0060]

[0061] in,

[0062] Step S3.3: Calculate the attitude angles, angular velocities, and angular accelerations relative to the roll axis and yaw axis of the inertial frame;

[0063] Inertial attitude roll angle and yaw angle ψ bi for

[0064]

[0065] The corresponding inertial Euler angular velocity and angular acceleration are:

[0066]

[0067]

[0068]

[0069]

[0070] Based on kinematics The inertial angular velocity can be obtained.

[0071]

[0072] Step S3.4: Calculate the pitch axis attitude;

[0073] Using the relationship between the attitude angles of the inertial frame and the attitude angles of the orbital frame, and the pitch angle constraint θ of the inertial frame... bi =0, determine the pitch angle θ of the orbital system, and have

[0074] A bi (A oi ) T =A bo

[0075] Among them, A bi It is the transformation matrix from the inertial frame to the home frame, expressed in terms of inertial attitude angles. Calculate A. bi (A oi ) T and with A bo By comparison

[0076]

[0077] in,

[0078] A oi,31 =-cosucosΩ+sinucosisinΩ

[0079] A oi,32 =-cosusinΩ-sinucosicosΩ

[0080] A oi,33 =-sinusini

[0081] Inertial angular velocity in the pitch direction The angular velocity of the pitch direction relative to the orbital system can be obtained.

[0082]

[0083] Furthermore, based on kinematic relationships,

[0084]

[0085] Differentiating gives

[0086]

[0087] in,

[0088] Compared with the prior art, the present invention has the following advantages:

[0089] This invention is applicable to situations where there are requirements for the camera's field of view during target observation, and can determine the desired attitude under specific field of view constraints. Attached Figure Description

[0090] Figure 1 This is a flowchart of a method for calculating the desired attitude trajectory of a satellite when observing a space target, according to the present invention.

[0091] Figure 2 A schematic diagram illustrating the relationship between Earth, satellites, and space targets. Detailed Implementation

[0092] The present invention will be further described below with reference to the accompanying drawings and by providing a detailed description of a preferred embodiment.

[0093] The main coordinate system is defined as follows.

[0094] Inertial coordinate system O i X i Y i Z i The origin is the Earth's center O. i The basic plane is the J2000.0 Earth-level horizontal equatorial plane; O i X i The vernal equinox point pointing from the Earth's center to J2000.0 within the fundamental plane; O i Z i The axis is the normal to the fundamental plane, pointing towards the North Pole; O i Y i With O i X i O i Z i The axes are perpendicular and form a right-handed coordinate system.

[0095] Satellite orbital coordinate system OX o Y o Z o The origin is the satellite's center of mass O; OX o The axis lies within the satellite's orbital plane and points in the direction of the satellite's motion; OZ o The axis points to the Earth's center; OY o With OX o OZo The axes are perpendicular and form a right-handed coordinate system.

[0096] Satellite body coordinate system OX b Y b Z b The origin is the satellite's center of mass O; when there is no attitude motion, OX b OY b OZ b The axes are respectively with OX o OY o OZ o The axes are parallel and in the same direction.

[0097] The following is based on Figure 1 The preferred embodiments of the present invention will be described in detail below.

[0098] like Figure 1 As shown, this invention provides a method for calculating the desired attitude trajectory of a satellite when observing a space target, comprising the following steps:

[0099] Step S1: Calculate the inertial vector of the satellite pointing towards the target and its representation in the orbital coordinate system;

[0100] Step S2: Calculate the desired attitude of the two axes other than the optical axis direction using the optical axis pointing constraint;

[0101] Step S3: Calculate the desired attitude along the optical axis using field-of-view constraints.

[0102] In step S1, calculating the satellite's inertial vector pointing towards the target and its representation in the orbital coordinate system includes:

[0103] Step S1.1: Calculate the satellite's vector coordinates in the orbital system;

[0104] The satellite's vector r pointing towards the Earth's center s In a satellite orbital system, it is represented as

[0105]

[0106] Here, the superscript 'o' indicates the description of the vector in the orbital frame, R s The orbital radius is calculated using the following formula.

[0107]

[0108] Where a, e, and f are the semi-major axis, eccentricity, and true anomaly angle of the satellite orbit, respectively. Considering the small eccentricity, the orbital radius R can be assumed to be... s If the changes are small, then the velocity and acceleration vectors in the orbital frame are available.

[0109]

[0110] Step S1.2: Calculate the target's vector coordinates in the inertial frame;

[0111] In this invention, the target's vector coordinates r are assumed to be... t Given that the representation in an inertial frame is denoted as r t i The superscript 'i' indicates the vector description in the inertial frame. The corresponding velocity and acceleration vectors in the inertial frame are denoted as... and

[0112] Step S1.3: Calculate the inertial vector of the satellite pointing towards the target and its representation in the orbital coordinate system;

[0113] Figure 2 This is a schematic diagram illustrating the relationship between Earth, satellites, and space targets, where r s The vector r represents the direction from which the satellite points towards the Earth's center. s represents the vector pointing from the Earth's center to the target, and 'l' represents the vector pointing from the satellite to the target, such as... Figure 2 As shown, based on the positional relationship between the satellite and the target, the vector l pointing from the satellite to the target can be represented in the orbital system.

[0114]

[0115] Among them, A oi The transformation matrix from the inertial frame to the orbital frame.

[0116]

[0117] Where u, i, and Ω represent the latitudinal argument, inclination, and right ascension of the ascending node of the satellite orbit, respectively.

[0118] For l o Differentiating gives

[0119]

[0120]

[0121] Where, ω oi =[0 -|ω0| 0] T Let ω0 be the projection of the angular velocity of the orbital frame relative to the inertial frame onto the orbital frame, where ω0 is the orbital angular velocity. For ω oi antisymmetric matrix

[0122]

[0123] The vector l pointing from the satellite to the target is represented in the inertial frame as:

[0124]

[0125] Differentiating with respect to time has

[0126]

[0127]

[0128] In step S2, calculating the desired attitude of the two axes other than the optical axis direction using the optical axis pointing constraint includes:

[0129] Step S2.1, calculate l o unit vector ρ o and its first and second derivatives;

[0130]

[0131]

[0132]

[0133] Step S2.2: Calculate the attitude angles, angular velocities, and angular accelerations of the roll axis and yaw axis;

[0134] According to the pointing constraint, the camera optical axis should be parallel to the target vector l during imaging. Assume the camera optical axis points towards the body + Y. b If the direction is such that the unit vector of the optical axis in this system is ρ, then... b =[0 1 0] T The superscript 'b' indicates the vector description within this system. If the Euler angle 312 transformation order is used to describe the satellite attitude, ρ can be obtained. b and relation

[0135]

[0136] Among them, A ob The attitude transformation matrix from the local system to the orbital system under the 312 transformation sequence is given by A. bo The transpose is obtained

[0137]

[0138] Then the attitude roll angle and yaw angle described in the orbital frame can be calculated.

[0139]

[0140]

[0141] Differentiating the above equation with respect to time yields the corresponding roll and yaw Euler angular velocities and angular accelerations.

[0142]

[0143]

[0144]

[0145]

[0146] According to the kinematic equations, the angular velocities of the roll and yaw directions relative to the orbital system are:

[0147]

[0148]

[0149] In step S3, calculating the desired attitude along the optical axis using field-of-view constraints includes:

[0150] Step S3.1: Determine the camera's field of view constraints;

[0151] When the optical axis points to the target, it can also rotate around itself, therefore other constraints are needed to determine the satellite's third attitude, namely its pitch attitude. Typically, for ease of image stitching, the camera must always be upright relative to the equatorial plane, meaning the horizontal central axis of the camera's field of view must be parallel to the equatorial plane. Therefore, the camera's field of view constraint can be understood as the roll axis OX. b It should be parallel to the inertial frame X. i O i Y i The plane, which is the inertial attitude pitch angle θ bi =0. Therefore, the pitch angular velocity and angular acceleration can be determined.

[0152] Step S3.2, calculate l i unit vector ρ i and its first and second derivatives;

[0153]

[0154]

[0155]

[0156] in,

[0157] Step S3.3: Refer to step S2.2 to calculate the attitude angles, angular velocities, and angular accelerations relative to the inertial frame of reference for the roll axis and yaw axis.

[0158] Inertial attitude roll angle and yaw angle ψ bi for

[0159]

[0160]

[0161] The corresponding inertial Euler angular velocity and angular acceleration are:

[0162]

[0163]

[0164]

[0165]

[0166] Then, based on the kinematic relationship, the inertial angular velocity can be obtained.

[0167]

[0168] Step S3.4: Calculate the pitch axis attitude;

[0169] Using the relationship between the attitude angles of the inertial frame and the attitude angles of the orbital frame, and the pitch angle constraint θ of the inertial frame... bi =0, determine the pitch angle θ of the orbital system, and have

[0170] A bi (A oi ) T =A bo

[0171] Among them, A bi This is the transformation matrix from the inertial frame to the home frame, expressed in terms of inertial attitude angles. Calculate A. bi (A oi ) T and with A bo By comparison

[0172]

[0173] in,

[0174] A oi,31 =-cosucosΩ+sinucosisinΩ

[0175] A oi,32 =-cosusinΩ-sinucosicosΩ

[0176] A oi,33 =-sinusini

[0177] Inertial angular velocity in the pitch direction The angular velocity of the pitch direction relative to the orbital system can be obtained.

[0178]

[0179] Furthermore, based on kinematic relationships,

[0180]

[0181] Differentiating gives

[0182]

[0183] in, At this point, the desired attitude information for attitude control during camera imaging has been obtained.

[0184] Although the present invention has been described in detail through the preferred embodiments above, it should be understood that the above description should not be considered as a limitation of the present invention. Various modifications and substitutions to the present invention will be apparent to those skilled in the art after reading the above description. Therefore, the scope of protection of the present invention should be defined by the appended claims.

Claims

1. A method for calculating the desired attitude trajectory of a satellite when observing a space target, characterized in that, Includes the following steps: Step S1: Calculate the inertial vector of the satellite pointing towards the target and its representation in the orbital coordinate system; Step S2: Calculate the desired attitude of the two axes other than the optical axis direction using the optical axis pointing constraint; Step S3: Calculate the desired attitude along the optical axis using field-of-view constraints; Step S1 specifically includes: Step S1.1: Calculate the satellite's vector coordinates in the orbital system; The satellite's vector pointing towards the Earth's center In a satellite orbital system, it is represented as Among them, the upper right corner mark ' o 'Indicates the description of a vector in an orbital frame. The orbital radius is calculated using the following formula: in, , and These represent the semi-major axis, eccentricity, and true anomaly angle of the satellite orbit, respectively. Considering the relatively small eccentricity, the orbital radius is assumed to be... If the changes are small, then the velocity and acceleration vectors in the orbital frame are: Step S1.2: Calculate the target's vector coordinates in the inertial frame; Assuming the target's vector coordinates Given that the representation in an inertial frame is denoted as The upper right corner is marked with ' i ' represents the description of a vector in an inertial frame, and the corresponding velocity and acceleration vectors in the inertial frame are denoted as ' and ; Step S1.3: Calculate the inertial vector of the satellite pointing towards the target and its representation in the orbital coordinate system; The vector pointing from the satellite to the target can be obtained based on the positional relationship between the satellite and the target. In the representation of orbital systems: in, The transformation matrix from the inertial frame to the orbital frame. in, , and These are the latitude argument, inclination, and right ascension of the ascending node of the satellite orbit, respectively. right Differentiating gives in, Let be the projection of the angular velocity of the orbital frame relative to the inertial frame onto the orbital frame. The orbital angular velocity, for antisymmetric matrix Satellite pointing to target vector In an inertial frame of reference, it is represented as Differentiating with respect to time has ； 。 2. The method for calculating the desired attitude trajectory of a satellite when observing a space target as described in claim 1, characterized in that, Step S2 specifically includes: Step S2.1, Calculation unit vector and its first and second derivatives; Step S2.2: Calculate the attitude angles, angular velocities, and angular accelerations of the roll axis and yaw axis; According to the pointing constraint, the camera optical axis should be aligned with the target vector during the imaging process. Parallel, assuming the camera's optical axis points towards the body. If the direction is such that the unit vector of the optical axis in this system is... The top right corner is marked with ' b ' represents the description of the vector in this system. Using Euler angles 312 transformation order to describe the satellite attitude, we can obtain... and relational formula in, The attitude transformation matrix from the local system to the orbital system under the 312 transformation sequence is given by... The transpose is obtained Then the attitude roll angle and yaw angle described in the orbital frame can be calculated. Differentiating the above equation with respect to time yields the corresponding roll and yaw Euler angular velocities and angular accelerations: According to the kinematic equations, the angular velocities of the roll and yaw directions relative to the orbital system are: ； 。 3. The method for calculating the desired attitude trajectory of a satellite when observing a space target as described in claim 1, characterized in that, Step S3 specifically includes: Step S3.1: Determine the camera's field of view constraints; When the optical axis points to the target, it can also rotate around itself. Therefore, other constraints are needed to determine the satellite's third attitude, namely its pitch attitude. To facilitate image stitching, the camera must always remain upright relative to the equatorial plane when taking pictures. That is, the horizontal central axis of the camera's field of view must be parallel to the equatorial plane. Therefore, the camera's field of view constraint can be understood as the roll axis. It should be parallel to the inertial frame of reference. The plane, also known as the inertial attitude pitch angle. From this, we can obtain the pitch angular velocity and angular acceleration. ; Step S3.2, Calculation unit vector and its first and second derivatives; in, ; Step S3.3: Calculate the attitude angles, angular velocities, and angular accelerations relative to the roll axis and yaw axis of the inertial frame; Inertial attitude roll angle and yaw angle for ； The corresponding inertial Euler angular velocity and angular acceleration are: Then, based on the kinematic relationship, the inertial angular velocity can be obtained. Step S3.4: Calculate the pitch axis attitude; By utilizing the relationship between the attitude angles of the inertial frame and the attitude angles of the orbital frame, as well as the pitch angle constraint of the inertial frame... Determine the pitch angle of the orbital system ,have in, It is the transformation matrix from the inertial frame to the home frame, expressed in terms of inertial attitude angles, and is calculated as follows: and By comparison in, Inertial angular velocity in the pitch direction The angular velocity of the pitch direction relative to the orbital system can be obtained. Furthermore, based on kinematic relationships, Differentiating gives in, .

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