A four-stage trajectory planning method for active push-broom imaging satellites

Abstract

A four-segment trajectory planning method for active push-scanning of an imaging satellite is disclosed. The planned motion trajectory is divided into an initial velocity elimination segment, a point-to-point maneuvering segment, a stationary segment, and an angular velocity preset segment in chronological order. The point-to-point maneuvering segment is further divided into an acceleration sub-segment, a uniform velocity sub-segment, and a deceleration sub-segment. The angular accelerations planned for the initial velocity elimination segment, the angular velocity preset segment, the acceleration sub-segment, and the deceleration sub-segment are sinusoidal functions. Then, the target attitude quaternion, target angular velocity, and target angular acceleration are determined for the time points of each segment and the entire time history.

Description

Technical Field

[0001] The present invention relates to a four-segment trajectory planning method for active push-scanning of an imaging satellite, and belongs to the technical field of spacecraft attitude maneuvering trajectory planning. Background Art

[0002] Highly maneuverable imaging satellites (HMISs) are highly maneuverable satellites capable of rapidly adjusting their attitude in space to accommodate diverse observation missions, thereby improving the efficiency and flexibility of observing ground targets. These satellites typically employ advanced attitude control technologies and systems, such as a high-output torque control gyro group that precisely and rapidly controls attitude maneuvers through angular momentum exchange. These satellites rapidly respond to attitude maneuver commands, enabling a variety of imaging modes, including on-track multi-point target imaging, on-track multi-strip stitching imaging, and on-track multi-angle imaging.

[0003] The active push-broom technology of highly maneuverable imaging satellites is an advanced on-orbit imaging technology that acquires images of ground targets in the desired path by actively performing attitude maneuvers. Unlike traditional passive push-broom imaging methods, active push-broom imaging does not rely solely on the satellite's orbital motion to achieve continuous acquisition of ground images. Instead, it actively controls the spatial pointing of the camera through satellite attitude maneuvers, thereby achieving rapid imaging of ground targets. Active push-broom technology is particularly suitable for observing narrow strips of targets that are not along the track, such as coastlines, boundaries, rivers, etc. Imaging of these targets can be completed within a single orbit, significantly improving imaging efficiency. Active push-broom technology can also be used for multi-strip stitching imaging of regional targets, achieving imaging coverage of targets in a larger area within the same time.

[0004] The process of transitioning a satellite from its current attitude to the initial attitude angle and angular velocity for active push-broom is called attitude pre-setting. The trajectory for attitude pre-setting requires pre-planning, and while satisfying multiple constraints, the trajectory duration must be a specified value or a minimum value. Currently, a commonly used trajectory planning method for active push-broom attitude pre-setting is the polynomial trajectory planning method. This method uses polynomials to describe the temporal evolution of the satellite's angle during attitude maneuvers. This method generates a smooth and continuous attitude change trajectory, ensuring smoother attitude closed-loop control during attitude control and avoiding increased control error or even oscillation caused by rapid changes in the target attitude. However, the polynomial trajectory planning method has drawbacks, such as underutilizing the satellite's maneuverability and difficulty calculating the maximum maneuvering angular velocity. The point-to-point sinusoidal trajectory planning method is also a commonly used planning method. It utilizes the smoothness of the sine function and its derivatives to design acceleration and deceleration segments of the attitude maneuver trajectory, smoothly connecting them with the intermediate constant angular velocity segment. However, this method is only applicable to maneuvers with zero angular velocity at both ends, i.e., point-to-point maneuvers. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to overcome the shortcomings of the existing technology and solve the problem of quickly and smoothly establishing the initial attitude and angular velocity of the imaging satellite's active push-scanning, thereby significantly improving the imaging satellite's ability and performance to perform active push-scanning missions.

[0006] The purpose of the present invention is achieved through the following technical solutions:

[0007] A four-segment trajectory planning method for active push-broom of an imaging satellite, comprising:

[0008] The motion trajectory is divided into the initial velocity elimination segment, point-to-point maneuvering segment, static segment and angular velocity preset segment in chronological order. The point-to-point maneuvering segment is divided into acceleration sub-segment, uniform speed sub-segment and deceleration sub-segment.

[0009] Calculate the time t for the initial velocity elimination stage dec , if the input specifies the time t for the attitude maneuver total , and t dec Greater than t total , then planning has no solution;

[0010] Calculate the time t for the preset angular velocity segment asc , if t dec +t asc ≥t total , then planning has no solution;

[0011] Calculate the initial and terminal attitude quaternions of the point-to-point maneuver segment based on the satellite attitude quaternions and three-axis angular velocity at the initial moment of the attitude maneuver and the satellite attitude quaternions and three-axis angular velocity at the terminal moment of the attitude maneuver;

[0012] Calculate the maximum angular velocity and the maximum angular acceleration of the point-to-point maneuvering segment; further determine the time t of the acceleration sub-segment and the deceleration sub-segment acc , time taken for uniform speed sub-segment t v If t dec +t asc +2t acc +t v >t total , then the planning has no solution, otherwise determine the time t for the stationary segment sta , the end time of the acceleration sub-segment t m1 , the end time t of the uniform speed sub-segment m2 , the end time t of the point-to-point maneuvering segment m3 ; Then, according to the order of initial velocity elimination section, point-to-point maneuvering section, stationary section and angular velocity preset section, the real-time target attitude quaternion, angular velocity and angular acceleration are calculated.

[0013] Compared with the prior art, the present invention has the following beneficial effects:

[0014] (1) Compared with the existing point-to-point sinusoidal trajectory planning method, the method of the present invention adds three new stages, namely, the initial velocity elimination stage, the static stage, and the angular velocity preset stage. This allows the attitude maneuver trajectory planning results to meet both the initial and terminal attitude angle constraints and the angular velocity constraints at the same time. The attitude angle and angular velocity trajectories are smooth and continuous, meeting the requirements of the angular momentum exchange device, and realizing the attitude preset function of the active push-sweep mission.

[0015] (2) The method of the present invention changes the attitude maneuver planning variable from the Euler angle of the existing method to the attitude quaternion, avoiding the singularity problem of the Euler angle, and changes the single-axis attitude maneuver planning to three-axis space maneuver planning, overcoming the limitations of the existing method. It is more convenient, safe and flexible to use on orbit, and can plan the attitude motion trajectory in the orbital system as well as the attitude motion trajectory in the inertial system, expanding the application scenarios.

[0016] (3) The method of the present invention plans the maximum angular velocity and angular acceleration of each maneuver through the ellipsoid envelope based on the maximum angular velocity and angular acceleration allowed by the three axes and the actual rotation axis of each segment, thereby fully utilizing the satellite's attitude maneuverability and ensuring the rapidity of the attitude maneuver.

[0017] (4) The method of the present invention can be externally specified or not, which increases the flexibility of application. If the duration is specified, the satellite can autonomously determine whether the mission can be completed based on its attitude maneuverability and provide a planning result when it is possible.

[0018] (5) The method of the present invention has been verified on multiple satellites in orbit and applied to various attitude maneuvering scenarios such as imaging satellites turning toward the Sun to active push-sweep, turning toward the Earth to active push-sweep, turning from active push-sweep to facing the Sun, turning from active push-sweep to facing the Earth, and turning from active push-sweep to active push-sweep. The planning results are short in time and have no safety risks.

[0019] (6) By utilizing the method of the present invention, the imaging satellite can quickly and reliably establish and exit the active push-scan attitude, thereby significantly enhancing the imaging capabilities of multiple targets on the same track, multi-strip splicing push-scanning, and multi-angle imaging. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1 This is a schematic diagram of the principle of the four-segment trajectory planning method for active push-scanning of an imaging satellite according to the present invention.

[0021] Figure 2 The present invention is a flowchart of the steps of the four-stage trajectory planning method for active push-scanning of an imaging satellite.

[0022] Figure 3 Schematic diagram of the angular velocity or angular acceleration ellipsoid envelope.

[0023] Figure 4 This is a curve diagram of satellite working mode.

[0024] Figure 5 This is a curve diagram of satellite attitude angle.

[0025] Figure 6 This is the satellite angular velocity curve. DETAILED DESCRIPTION

[0026] To make the objectives, technical solutions and advantages of the present invention more clear, the embodiments of the present invention will be described in further detail below with reference to the accompanying drawings.

[0027] In order to achieve rapid maneuvering of the imaging satellite's attitude under non-zero initial or target angular velocity conditions, the motion trajectory is pre-planned based on the initial angular velocity and target angular velocity during the maneuver and the integrated actuator capabilities, transforming the regulation control problem into a trajectory tracking control problem. The motion trajectory planned by the method of the present invention is divided into the initial velocity elimination section, the point-to-point maneuvering section, the static section, and the angular velocity preset section in chronological order. The point-to-point maneuvering section is further divided into three parts: the acceleration sub-section, the uniform velocity sub-section, and the deceleration sub-section. Figure 1 As shown in the figure, the angular accelerations planned for the initial velocity elimination, angular velocity preset, acceleration, and deceleration sub-segments are sinusoidal functions. The target attitude quaternion, angular velocity, and angular acceleration are calculated for each time point and the entire time history.

[0028] The specific implementation steps are as follows:

[0029] (1) Calculation of time required for initial velocity elimination

[0030] It is known that the satellite's three-axis angular velocity at the initial moment of the attitude maneuver is ω0. Calculate the modulus of the satellite's three-axis angular velocity at the initial moment of the attitude maneuver:

[0031] ω 0n =norm(ω0) (1)

[0032] Where norm() is the modulus function.

[0033] Calculate the unit vector of the module of the satellite's three-axis angular velocity at the initial moment of the attitude maneuver:

[0034] e tmp =unitize(ω0) (2)

[0035] In the formula, the subscript tmp indicates that the variable is a temporary variable, and the same applies below; unitize() is a function that normalizes a vector.

[0036] According to the angular acceleration ellipse envelope of the satellite attitude maneuverability, such as Figure 3 As shown, calculate the maximum angular acceleration in the initial velocity elimination stage:

[0037]

[0038] Where [0], [1], and [2] represent the components of the vector, starting from 0, and the same applies to the following; a ManMax is the maximum maneuvering angular acceleration of the satellite in three axes, which is a known quantity.

[0039] The modulus of the satellite's three-axis angular velocity at the initial moment of the attitude maneuver is ω 0n The maximum angular acceleration a during the initial velocity elimination phase dec Calculate the time taken to eliminate the initial velocity:

[0040]

[0041] Where π is the circular constant.

[0042] If the input specifies the time t for attitude maneuvers total , then judge t dec Is it greater than t total , if t dec ≥t total Then the planning has no solution and the planning method is exited directly. If t dec <t total Then proceed to step 2 below. If the input does not specify the time t for the attitude maneuver total , then continue to step 2 below.

[0043] (2) Calculate the time taken for the angular velocity preset segment

[0044] The three-axis target angular velocity of the satellite at the terminal moment of the known attitude maneuver is ω t , calculate the modulus of the satellite's three-axis target angular velocity at the attitude maneuver terminal moment:

[0045] ω tn =norm(ω t ) (5)

[0046] Calculate the modulus of the satellite's three-axis target angular velocity at the attitude maneuver terminal moment:

[0047] e tmp =unitize(ω0) (6)

[0048] According to the angular acceleration ellipse envelope of the satellite attitude maneuverability, the maximum angular acceleration of the angular velocity preset segment is calculated:

[0049]

[0050] The modulus of the satellite's three-axis target angular velocity at the attitude maneuver terminal is ω tn and the maximum angular acceleration a of the angular velocity preset segment asc Calculate the time taken for the angular velocity preset segment:

[0051]

[0052] If the input specifies the time t for attitude maneuvers total , then determine the time t used in the angular velocity preset segment dec Is the time taken for the angular velocity preset segment greater than t? total , if t dec +t asc ≥t total Then the planning has no solution and the planning method is exited directly. If t dec +t asc <t total Then proceed to step 3 below. If the input does not specify the time t for the attitude maneuver total , then continue to step 3 below.

[0053] (3) Calculate the initial and terminal attitude quaternions of point-to-point maneuvers

[0054] If the module of the satellite's three-axis angular velocity at the initial moment of the attitude maneuver is ω 0n >0, then calculate the initial attitude quaternion q of the point-to-point maneuver according to the following formula in :

[0055]

[0056] q in =qMult(q0,q tmp ) (10)

[0057] Wherein, the AxisAng2q(a,Φ) function represents the calculation of the attitude quaternion corresponding to the rotation angle Φ around the vector a. Its algorithm is well known in the art and will not be described in detail in this invention. The qMult() function is the attitude quaternion multiplication function. Its algorithm is well known in the art and will not be described in detail in this invention. q0 is the attitude quaternion at the initial moment of the attitude maneuver.

[0058] If the module of the satellite's three-axis angular velocity at the initial moment of the attitude maneuver is ω 0n = 0, then calculate the initial attitude quaternion q of the point-to-point maneuver according to the following formula in :

[0059] Let q in =q0(11)

[0060] If the module ω of the satellite's three-axis target angular velocity at the attitude maneuver terminal moment is tn >0, then calculate the point-to-point maneuver terminal attitude quaternion q as follows out :

[0061]

[0062] q out =qMult(q t ,qtmp ) (13)

[0063] Where q t is the attitude quaternion at the end of attitude maneuver.

[0064] If the module of the satellite's three-axis angular velocity at the end of the attitude maneuver is ω tn = 0, then calculate the point-to-point maneuver terminal attitude quaternion q as follows out :

[0065] Let q out =q t (14)

[0066] Calculate the axis of rotation e and angle χ for a point-to-point maneuver:

[0067] [e,χ]=q2AxisAng(qDiv(q in ,q out )) (15)

[0068] In the formula, qDiv() is the attitude quaternion division operation function, and its algorithm is well known in the art and will not be introduced in detail in the present invention; q2AxisAng() is the corresponding axis and angle calculated by the attitude quaternion, which is the opposite process of the aforementioned function AxisAng2q(). Its algorithm is well known in the art and will not be introduced in detail in the present invention.

[0069] Then continue to step 4 below.

[0070] (4) Calculation of point-to-point maneuvering time

[0071] First, based on the angular velocity ellipse envelope of the satellite's attitude maneuverability, the maximum angular velocity of the point-to-point maneuver segment is calculated:

[0072]

[0073] Where, ω ManMax is the maximum maneuvering angular velocity of the satellite in three axes, which is a known quantity.

[0074] Then, based on the angular acceleration ellipse envelope of the satellite attitude maneuverability, the maximum angular acceleration of the point-to-point maneuver segment is calculated:

[0075]

[0076] Then, calculate the time taken for the acceleration and deceleration sub-segments in the point-to-point maneuvering segment:

[0077]

[0078] Then, calculate the time of the uniform speed sub-segment in the point-to-point maneuvering segment:

[0079]

[0080] If t v <0, the time t taken for the acceleration and deceleration sub-segments in the point-to-point maneuvering segment is acc , and the time t for the uniform speed segment v Use the following formula instead:

[0081]

[0082] t v =0 (21)

[0083] If the input specifies the time t for attitude maneuvers total , then judge t dec +t asc +2t acc +t v Is it greater than t total , if t dec +t asc +2t acc +t v >t total If there is no solution to the planning, exit the planning method directly.

[0084] If t dec +t asc +2t acc +t v ≤t total , then continue to calculate the static segment time as follows:

[0085] t sta =t total -(t dec +t asc +2t acc +t v ) (twenty two)

[0086] If the input does not specify the time t for attitude maneuver total , then the static period takes time t sta Take it as 0.

[0087] Then, calculate the end time of the acceleration sub-segment of the point-to-point maneuvering segment:

[0088] t m1 =t dec +t acc (twenty three)

[0089] Then, calculate the end time of the uniform speed sub-segment of the point-to-point maneuvering segment:

[0090] t m2 =t dec +tacc +t v (twenty four)

[0091] Afterwards, calculate the end time of the point-to-point maneuver segment:

[0092] t m3 =t dec +2t acc +t v (25)

[0093] Then continue to step 5 below.

[0094] (5) Calculate real-time target attitude quaternion, angular velocity and angular acceleration

[0095] The difference between the current onboard time and the start time of attitude maneuver is t m The following will be based on t m The calculation formula of the real-time target attitude quaternion q, target angular velocity ω and target angular acceleration a is determined by the value of

[0096] If t m If ≤0, the attitude maneuver has not started, and the real-time target attitude quaternion q, target angular velocity ω, and target angular acceleration a are calculated as follows:

[0097] q=ω0 (26)

[0098] ω=ω0 (27)

[0099] a=[0 0 0] T (28)

[0100] Where T is the transposition operator symbol.

[0101] Otherwise, if t m <t dec , then it is currently in the initial velocity elimination stage, and the real-time target attitude quaternion q, target angular velocity ω, and target angular acceleration a are calculated as follows:

[0102]

[0103] q tmp =AxisAng2q(ω0,χ r ) (32)

[0104] q=qMult(q0,q tmp ) (33)

[0105]

[0106] a=a r unitize(ω0) (35)

[0107] Where a r 、 χ r and q tmp They are all intermediate variables in the calculation, so their physical meanings will not be introduced in detail; sin() is the sine function; cos() is the cosine function.

[0108] Otherwise, if t m <t m1 , then in the acceleration sub-segment of the point-to-point maneuvering segment, the real-time target attitude quaternion q, target angular velocity ω, and target angular acceleration a are calculated as follows:

[0109] t tmp =t m -t dec (36)

[0110]

[0111] q tmp =AxisAng2q(e,χ r ) (40)

[0112] q=qMult(q in ,q tmp ) (41)

[0113]

[0114] a=a r e (43)

[0115] Where, t tmp is the intermediate variable in the calculation.

[0116] Otherwise, if t m <t m2 , then the current uniform speed sub-segment in the point-to-point maneuvering segment, the real-time target attitude quaternion q, target angular velocity ω and target angular acceleration a are calculated as follows:

[0117] a r =0 (44)

[0118]

[0119] q tmp =AxisAng2q(e,X r ) (47)

[0120] q=qMult(q in ,q tmp ) (48)

[0121]

[0122] a=a r e (50)

[0123] Otherwise, if t m <t m3 , then the current point-to-point maneuvering segment is in the deceleration sub-segment, and the real-time target attitude quaternion q, target angular velocity ω, and target angular acceleration a are calculated as follows:

[0124] t tmp =t m -t m2 (51)

[0125]

[0126]

[0127] q tmp =AxisAng2q(e,χ r ) (55)

[0128] q=qMult(q in ,q tmp ) (56)

[0129]

[0130] a=a r e (58)

[0131] Otherwise, if t m <t m3 +t sta , then it is currently in the static segment, and the real-time target attitude quaternion q, target angular velocity ω and target angular acceleration a are calculated as follows:

[0132] q=q out (59)

[0133] ω=[0 0 0] T (60)

[0134] a=[0 0 0] T (61)

[0135] Otherwise, if t m <t m3 +t sta +t asc , then the current state is in the angular velocity preset section, and the real-time target attitude quaternion q, target angular velocity ω, and target angular acceleration a are calculated as follows:

[0136] t tmp =t m -(tm3 +t sta ) (62)

[0137]

[0138] q tmp =AxisAng2q(ω t ,χ r ) (66)

[0139] q=qMult(q out ,q tmp ) (67)

[0140]

[0141] a=a r unitize(ω t ) (69)

[0142] If none of the above conditions are met, the attitude maneuver process is completed, and the real-time target attitude quaternion q, target angular velocity ω, and target angular acceleration a are calculated as follows:

[0143] q=q t (70)

[0144] ω=ω t (71)

[0145] a=[0 0 0] T (72)

[0146] Step 5 is executed once per control cycle on the satellite until t m ≥t m3 +t sta +t asc until.

[0147] The mathematical simulation results of the method of the present invention are as follows Figures 4 to 6 As shown, the posture maneuver from active push-sweep to active push-sweep is taken as an example. Figure 4 It is the mode character curve. The value 13 indicates the active push-sweep mode, and the value 12 indicates the attitude preset mode. Figure 5 is the attitude angle curve. It can be seen from it that there is a difference of about 50° in the attitude angle before and after attitude preset, indicating that a large-angle attitude maneuver has been completed. Figure 6 The angular velocity curve shows that the angular velocity at the end of the previous active push-sweep is non-zero, approximately 1.6° / s, while the angular velocity at the start of the next active push-sweep is approximately 0.6° / s. This simulation result shows that the attitude maneuver trajectory planned by the proposed method simultaneously satisfies the three-axis angle and angular velocity constraints at both ends.

[0148] The contents not described in detail in the specification of the present invention belong to the common knowledge of those skilled in the art.

[0149] Although the present invention has been disclosed above in terms of preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art may make possible changes and modifications to the technical solutions of the present invention by using the methods and technical contents disclosed above without departing from the spirit and scope of the present invention. Therefore, any simple modifications, equivalent changes and modifications made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solutions of the present invention shall fall within the scope of protection of the technical solutions of the present invention.

Claims

1. A four-stage trajectory planning method for active push-broom imaging satellites, characterized in that: include: The motion trajectory is divided into the initial velocity elimination segment, point-to-point maneuvering segment, static segment and angular velocity preset segment in chronological order. The point-to-point maneuvering segment is divided into acceleration sub-segment, uniform speed sub-segment and deceleration sub-segment. Calculate the time t for eliminating initial velocity dec , if the input specifies the time t for the attitude maneuver total , and t dec Greater than t total , then planning has no solution; Calculate the time t for the preset angular velocity segment asc , if t dec +t asc ≥t total , then planning has no solution; Calculate the initial and terminal attitude quaternions of the point-to-point maneuver segment based on the satellite attitude quaternions and three-axis angular velocity at the initial moment of the attitude maneuver and the satellite attitude quaternions and three-axis angular velocity at the terminal moment of the attitude maneuver; Calculate the maximum angular velocity and the maximum angular acceleration of the point-to-point maneuvering segment; further determine the time t of the acceleration sub-segment and the deceleration sub-segment acc , time taken for uniform speed sub-segment t v ; if t dec +t asc +2t acc +t v >t total , then the planning has no solution, otherwise determine the time t for the stationary segment sta , the end time of the acceleration sub-segment t m1 , the end time t of the uniform speed sub-segment m2 , the end time t of the point-to-point maneuvering segment m3 ; Then, according to the order of initial velocity elimination section, point-to-point maneuvering section, stationary section and angular velocity preset section, the real-time target attitude quaternion, angular velocity and angular acceleration are calculated.

2. The four-stage trajectory planning method for active push-broom of an imaging satellite according to claim 1, characterized in that: Time for eliminating initial velocity t dec for: e tmp =unitize(ω0) oh 0n =norm(ω0) Where norm() is the modulus function; the subscript tmp indicates that the variable is a temporary variable, unitize() is the function that normalizes the vector; [0], [1], [2] represent the components of the vector, starting from 0, the same below; a ManMax is the maximum angular acceleration of the satellite's three-axis maneuvering, which is a known quantity; π is the pi constant, and ω0 is the satellite's three-axis angular velocity at the initial moment of the attitude maneuver.

3. The four-stage trajectory planning method for active push-broom of an imaging satellite according to claim 2, characterized in that: Angular velocity preset time t asc for: e tmp =unitize(ω0) oh tn =norm(ω t ) ω t is the satellite's three-axis target angular velocity at the attitude maneuver terminal moment.

4. The four-stage trajectory planning method for active push-broom of an imaging satellite according to claim 1, characterized in that: Calculating the initial and terminal attitude quaternions for the point-to-point maneuver segment involves: If the module of the satellite's three-axis angular velocity at the initial moment of the attitude maneuver is ω 0n >0, then calculate the initial attitude quaternion q of the point-to-point maneuver according to the following formula in : q in =qMult(q0,q tmp ) Wherein, AxisAng2q(a,Φ) function represents the calculation of the attitude quaternion corresponding to the rotation angle Φ around the vector a; qMult() function is the attitude quaternion multiplication function; q0 is the attitude quaternion at the initial moment of the attitude maneuver; If the module of the satellite's three-axis angular velocity at the initial moment of the attitude maneuver is ω 0n = 0, then calculate the initial attitude quaternion q of the point-to-point maneuver according to the following formula in : Let q in =q0 If the module ω of the satellite's three-axis target angular velocity at the attitude maneuver terminal moment is tn >0, then calculate the point-to-point maneuver terminal attitude quaternion q as follows out : q out =qMult(q t ,q tmp ) Where q t is the attitude quaternion at the end of attitude maneuver; If the module of the satellite's three-axis angular velocity at the end of the attitude maneuver is ω tn = 0, then calculate the point-to-point maneuver terminal attitude quaternion q as follows out : Let q out =q t Calculate the axis of rotation e and angle χ for a point-to-point maneuver: [e,χ]=q2AxisAng(qDiv(q in ,q out )) Where qDiv() is the attitude quaternion division function; q2AxisAng() is the axis and angle calculated from the attitude quaternion, which is the opposite process of the function AxisAng2q().

5. The four-stage trajectory planning method for active push-broom of an imaging satellite according to claim 1, characterized in that: The time taken for the acceleration and deceleration sub-segments is t acc for: According to the angular velocity ellipse envelope of the satellite's attitude maneuverability, the maximum angular velocity of the point-to-point maneuver segment is calculated: Where, ω ManMax is the maximum angular velocity of the satellite's three-axis maneuver, which is a known quantity; e is the axis of rotation for point-to-point maneuvers; [0], [1], [2] represent the components of the vector, starting from 0; According to the angular acceleration ellipse envelope of the satellite attitude maneuverability, the maximum angular acceleration of the point-to-point maneuver segment is calculated: a ManMax is the maximum maneuvering angular acceleration of the satellite in three axes; Calculate the time taken for the acceleration and deceleration sub-segments in the point-to-point maneuver segment:

6. The four-stage trajectory planning method for active push-broom of an imaging satellite according to claim 5, characterized in that: The time t of the uniform speed sub-segment in the point-to-point maneuvering segment v for: X is the point-to-point maneuvering angle; If t v <0, the time t taken for the acceleration and deceleration sub-segments in the point-to-point maneuvering segment is acc , and the time t for the uniform speed segment v Use the following formula instead: t v ＝0。 7. The four-stage trajectory planning method for active push-broom of an imaging satellite according to claim 6, characterized in that: If t dec +t asc +2t acc +t v ≤t total , then continue to calculate the static segment time as follows: t sta =t total -(t dec +t asc +2t acc +t v )。 8. The four-stage trajectory planning method for active push-broom of an imaging satellite according to claim 7, characterized in that: If the input does not specify the time t for attitude maneuver total , then the static period takes time t sta Take it as 0; Calculate the end time of the acceleration subsegment of the point-to-point maneuver segment: t m1 =t dec +t acc Calculate the end time of the uniform velocity subsegment of the point-to-point maneuver segment: t m2 =t dec +t acc +t v Calculate the end time of the point-to-point maneuver segment: t m3 =t dec +2t acc +t v 。 9. The four-stage trajectory planning method for active push-broom of an imaging satellite according to claim 8, characterized in that: The difference between the current onboard time and the start time of attitude maneuver is t m , according to t m The calculation formula of the real-time target attitude quaternion q, target angular velocity ω and target angular acceleration a is determined by the value of: If t m If ≤0, the attitude maneuver has not started, and the real-time target attitude quaternion q, target angular velocity ω, and target angular acceleration a are calculated as follows: q=q0 ω=ω0 a＝[0 0 0] T Where, T is the transposition operator symbol; Otherwise, if t m <t dec , then it is currently in the initial velocity elimination stage, and the real-time target attitude quaternion q, target angular velocity ω, and target angular acceleration a are calculated as follows: q tmp =AxisAng2q(ω0,x r ) q=qMult(q0,q tmp ) a=a r unitize(ω0) Where a r 、 X r and q tmp Both are intermediate variables for calculation; sin() is the sine function; cos() is the cosine function; Otherwise, if t m <t m1 , then in the acceleration sub-segment of the point-to-point maneuvering segment, the real-time target attitude quaternion q, target angular velocity ω, and target angular acceleration a are calculated as follows: t tmp =t m -t dec q tmp =AxisAng2q(e,χ r ) q=qMult(q in ,q tmp ) a=a r and Where, t tmp is the intermediate variable of the calculation; Otherwise, if t m <t m2 , then the current uniform speed sub-segment in the point-to-point maneuvering segment, the real-time target attitude quaternion q, target angular velocity ω and target angular acceleration a are calculated as follows: a r ＝0 q tmp =AxisAng2q(e,χ r ) q=qMult(q in ,q tmp ) a=a r and Otherwise, if t m <t m3 , then the current deceleration sub-segment in the point-to-point maneuvering segment, the real-time target attitude quaternion q, target angular velocity ω and target angular acceleration a are calculated as follows: t tmp =t m -t m2 q tmp =AxisAng2q(e,χ r ) q=qMult(q in ,q tmp ) a=a r and Otherwise, if t m <t m3 +t sta , then it is currently in the static segment, and the real-time target attitude quaternion q, target angular velocity ω and target angular acceleration a are calculated as follows: q=q out ω=[0 0 0] T a＝[0 0 0] T Otherwise, if t m <t m3 +t sta +t asc , then the current state is in the angular velocity preset section, and the real-time target attitude quaternion q, target angular velocity ω, and target angular acceleration a are calculated as follows: t tmp =t m -(t m3 +t sta ) q tmp =AxisAng2q(ω t ,x r ) q=qMult(q out ,q tmp ) a=a r unitize(ω t ) If none of the above conditions are met, the attitude maneuver process is completed, and the real-time target attitude quaternion q, target angular velocity ω, and target angular acceleration a are calculated as follows: q=q t oh = oh t a＝[0 0 0] T 。 10. A computer program product stored on a non-transitory computer-readable medium, the computer program product comprising program code for carrying out the method according to any one of claims 1 to 9.

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