Four-segment trajectory planning method for active push-broom of imaging satellite

Abstract

A four-segment trajectory planning method for active push-broom of an imaging satellite is characterized in that a planned motion trajectory is divided into an initial speed elimination segment, a point-to-point maneuvering segment, a stationary segment and an angular speed preset segment according to a time sequence, and the point-to-point maneuvering segment is divided into an acceleration sub-segment, a constant speed sub-segment and a deceleration sub-segment; angular accelerations planned by the initial speed elimination section, the angular speed preset section, the acceleration sub-section and the deceleration sub-section are sine functions; then determining the time point of each section and the target attitude quaternion, the target angular velocity and the target angular acceleration of the whole time history;

Description

Technical Field

[0001] The 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 maneuver trajectory planning. Background Art

[0002] A highly maneuverable satellite is a satellite that can quickly adjust its attitude in space to adapt to different observation tasks, thereby improving the efficiency and flexibility of observing ground targets. Highly maneuverable imaging satellites usually use advanced attitude control technologies and systems, such as using a group of control torque gyroscopes with large output torque to accurately and quickly control attitude maneuvers through angular momentum exchange. Highly maneuverable imaging satellites respond quickly to attitude maneuvering commands and achieve multiple imaging modes such as imaging of multiple points on the same track, imaging of multiple strips on the same track, and imaging of multiple angles on the same track.

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

[0004] The process of changing the satellite from the current attitude to the initial attitude angle and angular velocity for active push-scanning is called attitude preset. The trajectory of attitude preset needs to be planned in advance. Under the premise of satisfying multiple constraints, the duration of the trajectory is a specified value or a minimum value. At present, a commonly used trajectory planning method for attitude preset of active push-scanning is the polynomial trajectory planning method. This method uses polynomials to describe the change law of the satellite's angle over time during the attitude maneuver, and can generate a smooth and continuous attitude change trajectory, so that the attitude closed-loop control of the satellite is more stable when performing attitude control, avoiding the problem of increased control error or even oscillation caused by rapid changes in the target attitude. However, the polynomial trajectory planning method has the disadvantages of not fully utilizing the satellite's maneuverability and difficulty in calculating the maximum maneuvering angular velocity. The point-to-point sinusoidal trajectory planning method is also a commonly used planning method. It uses the smoothness of the sine function and its derivatives to design the acceleration and deceleration segments of the attitude maneuvering trajectory, which are smoothly connected with the uniform angular velocity segment in the middle. However, this method is only applicable to maneuvers with zero angular velocity at both ends, that is, point-to-point maneuvers. Summary of the invention

[0005] The technical problem to be solved by the present invention is to overcome the deficiencies of the prior art and solve the problem of rapid and stable establishment of the initial attitude and angular velocity of the active push-scanning imaging satellite, thereby significantly improving the ability and performance of the imaging satellite to perform active push-scanning tasks.

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

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

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

[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 of the angular velocity preset 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 maneuvering 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 maneuvering.

[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 , uniform speed sub-segment time t v ; if t dec +t asc +2t acc +t v >t total , then the planning has no solution, otherwise determine the static segment time t 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 of the point-to-point maneuvering segment t m3 ; Then, in the order of initial velocity elimination stage, point-to-point maneuvering stage, stationary stage and angular velocity preset stage, 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, so that the attitude maneuver trajectory planning result can not only meet the initial and terminal attitude angle constraints, but also meet the angular velocity constraints at the same time. The attitude angle and angular velocity trajectories are smooth and continuous, meeting the use requirements of the angular momentum exchange device, and realizing the attitude preset function of the active push-sweep task.

[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, thereby avoiding the singularity problem of the Euler angle, and changes the single-axis attitude maneuver planning to the three-axis space maneuver planning, thereby overcoming the limitations of the existing method. The method 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, thus 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 according to the maximum angular velocity and angular acceleration allowed by the three axes and the actual rotation axis of each segment, thereby making full use of 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 improves the flexibility of application. If the duration is specified, the satellite can autonomously determine whether the task can be completed based on its attitude maneuvering capability, and provide a planning result when it can be completed.

[0018] (5) The method of the present invention has been verified in orbit by multiple satellites and applied to various posture 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 the sun, turning from active push-sweep to 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 using the method of the present invention, the imaging satellite can realize the rapid and reliable establishment and exit of active push-scan attitude, so that the imaging capabilities of multi-point targets on the same track, multi-strip splicing push-scanning, and multi-angle imaging are significantly enhanced. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1 The schematic diagram is a schematic diagram of the four-stage 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 satellite attitude angle curve.

[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 further described in detail below with reference to the accompanying drawings.

[0027] In order to realize the rapid maneuvering of the attitude of the imaging satellite under the condition of non-zero initial or target angular velocity, the motion trajectory is pre-planned according to the initial angular velocity and target angular velocity during the maneuver and the integrated actuator capability, and the regulation control problem is converted into a trajectory tracking control problem. The motion trajectory planned by the method of the present invention is divided into an initial velocity elimination section, a point-to-point maneuvering section, a stationary section and an angular velocity preset section in chronological order, wherein the point-to-point maneuvering section is further divided into three parts: an acceleration sub-section, a uniform speed sub-section and a deceleration sub-section, such as Figure 1 As shown in the figure, the angular accelerations planned for the initial velocity elimination segment, angular velocity preset segment, acceleration sub-segment, and deceleration sub-segment are sinusoidal functions. The target attitude quaternion, angular velocity, and angular acceleration are calculated at the time points of each segment 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. The same applies to the following text. 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] In the formula, π is the circular constant.

[0042] If the input specifies the time t for the attitude maneuver 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 directly exited. 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 required for the angular velocity preset segment

[0044] The three-axis target angular velocity of the satellite at the known attitude maneuver terminal 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 the attitude maneuver total , then determine the time t used for 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 directly exited. 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 modulus of the satellite's three-axis angular velocity at the initial moment of the attitude maneuver is 0n >0, then calculate the initial attitude quaternion q of the point-to-point maneuver as follows in :

[0055]

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

[0057] In the formula, the AxisAng2q(a,Φ) function represents the calculation of the attitude quaternion corresponding to the rotation angle Φ around the vector a, and its algorithm is well known in the art and will not be introduced in detail in the present invention; the qMult() function is the attitude quaternion multiplication function, and its algorithm is well known in the art and will not be introduced in detail in the present invention; q0 is the attitude quaternion at the initial moment of the attitude maneuver.

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

[0059] Let q in =q0(11)

[0060] If the modulus of the satellite's three-axis target angular velocity at the end of the attitude maneuver 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] In the formula, q t is the attitude quaternion at the end of attitude maneuver.

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

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

[0066] Calculate the rotation axis 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(), and 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 attitude maneuverability, the maximum angular velocity of the point-to-point maneuvering segment is calculated:

[0072]

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

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

[0075]

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

[0077]

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

[0079]

[0080] If t v <0, the time taken for the acceleration and deceleration sub-segments in the point-to-point maneuvering segment is t acc , and the time t of 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 the attitude maneuver 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 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 for the attitude maneuver, t total , then the static period takes time t sta Take it as 0.

[0087] After that, 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] After that, 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] After that, calculate the end time of the point-to-point maneuvering 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 the attitude maneuver is t m The following will be based on t m The value of is used to determine the calculation formula of the real-time target attitude quaternion q, target angular velocity ω and target angular acceleration a.

[0096] If m ≤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] In the formula, 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 the current acceleration 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:

[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 it is currently 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 ,x 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 over, 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 in each 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 a mode character curve, the value 13 indicates active push-sweep mode, and the value 12 indicates attitude preset mode. Figure 5 is the attitude angle curve, from which we can see that there is a difference of about 50° in the attitude angle before and after the attitude preset, indicating that the large-angle attitude maneuver is completed. Figure 6 is the angular velocity curve, from which we can see that the angular velocity at the end of the last active push sweep is non-zero, about 1.6° / s, and the angular velocity at the beginning of the next active push sweep is about 0.6° / s. The simulation results show that the attitude maneuver trajectory planned by the method of the present invention satisfies the three-axis angle and angular velocity constraints at both ends at the same time.

[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 as above in the form of a preferred embodiment, it is not intended to limit the present invention. Any person skilled in the art may make possible changes and modifications to the technical solution 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 solution of the present invention shall fall within the protection scope of the technical solution of the present invention.

Claims

1. A four-stage trajectory planning method for active push-scanning of an imaging satellite, characterized in that: include: The motion trajectory is divided into the initial velocity elimination section, point-to-point maneuvering section, static section and angular velocity preset section in chronological order, among which the point-to-point maneuvering section is divided into acceleration sub-section, uniform speed sub-section and deceleration sub-section; 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; Calculate the time t of the angular velocity preset 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 maneuvering 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 maneuvering. 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 , uniform speed sub-segment time t v ; if t dec +t asc +2t acc +t v >t total , then the planning has no solution, otherwise determine the static segment time t sta , the end time of the acceleration segment t m1 , the end time t of the uniform speed sub-segment m2 , the end time of the point-to-point maneuvering segment t m3 ; Then, in the order of initial velocity elimination stage, point-to-point maneuvering stage, stationary stage and angular velocity preset stage, the real-time target attitude quaternion, angular velocity and angular acceleration are calculated.

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

5. The four-stage trajectory planning method for active push-scanning 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 attitude maneuverability, the maximum angular velocity of the point-to-point maneuvering segment is calculated: In the formula, ω ManMax is the maximum angular velocity of the satellite's three-axis maneuver, which is a known quantity; e is the rotation axis of the point-to-point maneuver; [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 maneuvering segment:

6. The four-stage trajectory planning method for active push-scanning of an imaging satellite according to claim 5, characterized in that: The time taken for the uniform speed sub-segment in the point-to-point maneuvering segment is t v for: X is the point-to-point maneuvering angle; If t v <0, the time taken for the acceleration and deceleration sub-segments in the point-to-point maneuvering segment is t acc , and the time t of the uniform speed segment v Use the following formula instead: t v ＝0。 7. The four-stage trajectory planning method for active push-scanning of an imaging satellite according to claim 6, characterized in that: If dec +t asc +2t acc +t v ≤t total , then continue to calculate the static 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-scanning of an imaging satellite according to claim 7, characterized in that: If the input does not specify the time for the attitude maneuver, t 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-scanning of an imaging satellite according to claim 8, characterized in that: The difference between the current onboard time and the start time of the attitude maneuver is t m , according to t m The value of is used to determine the calculation formula of the real-time target attitude quaternion q, target angular velocity ω and target angular acceleration a: If m ≤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 In the formula, 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) In the formula, a r , X r and q tmp They are all intermediate variables for calculation; sin() is the sine function; cos() is the cosine function; Otherwise, if t m <t m1 , then the current acceleration 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 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 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: 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 it is currently 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 over, 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 a program code for carrying out the method according to any one of claims 1 to 9.

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