An Agile and Safe Segmented Trajectory Planning Method for Spacecraft

Abstract

An agile and safe segmented trajectory planning method for spacecraft, combining the characteristics of sine trajectory planning that the maximum angular velocity and maximum angular acceleration can be known in advance, proposes a trajectory planning method with two / three segments from any attitude to the desired angle and desired angular velocity. The planned trajectory can achieve that the maximum angular velocity and angular acceleration can be known in advance, and in most cases, the time is shorter than polynomial planning, which is applicable to spacecraft with agile maneuvering and multi-mode imaging requirements.

Description

Technical Field

[0001] The present invention belongs to the technical field of spacecraft attitude control and relates to a spacecraft trajectory planning method. Background Art

[0002] With the continuous improvement of the requirements for high-resolution remote sensing and on-orbit services, the demand for agile maneuverability of contemporary large satellite platforms is increasing. For the tracking problem of a given fixed curve or dynamic target, it is desired that the spacecraft synchronize with the angular velocity of the tracked target at the moment of tracking the fixed curve or dynamic target to achieve more accurate tracking.

[0003] The traditional polynomial planning method cannot know in advance the value of the maximum angular velocity, which makes the spacecraft at risk of abnormal situations due to insufficient maneuverability. Therefore, it is necessary to propose a new trajectory planning method with strong safety to establish the end angle and angular velocity of the trajectory planning simultaneously, and the maximum angular velocity can be known in advance during the maneuvering process. Summary of the Invention

[0004] The technical problem solved by the present invention is: overcoming the deficiencies of the prior art, a spacecraft agile and safe segmented trajectory planning method is proposed. For the attitude maneuvering problem with the requirement of establishing the end angle and angular velocity simultaneously, by decomposing the entire maneuvering process into two / three segments, calculating the total maneuvering time in advance according to the maneuvering ability, and then judging whether to perform the attitude maneuver, the safety of the spacecraft is greatly improved. At the same time, the entire trajectory of the maneuver is known in advance, and the complete control of the maneuvering process can be achieved.

[0005] The technical solution of the present invention is: a spacecraft agile and safe segmented trajectory planning method, which performs two-stage or three-stage planning on the spacecraft motion trajectory according to whether the three-axis attitude angular velocity of the spacecraft at the trajectory planning starting point is 0. If the three-axis attitude angular velocity of the spacecraft at the trajectory planning starting point is 0, a two-stage planning of a point-to-point maneuver segment and an acceleration segment is adopted for the spacecraft motion trajectory. If the three-axis attitude angular velocity of the spacecraft at the trajectory planning starting point is not 0, a three-stage planning of a deceleration segment, a point-to-point maneuver segment, and an acceleration segment is adopted for the spacecraft motion trajectory.

[0006] Further, in the deceleration segment, the spacecraft is controlled to maneuver an angle χ around the Euler axis Axis1 dw , to achieve deceleration of the spacecraft, where:

[0007] Axis1 = [ω dw [1] / nω dw , ω dw [2] / nω dw , ω dw [3] / nω dw ​

[0008]

[0009] nω dw =|ω dw |

[0010] dEuler2wbo() is the attitude kinematic function that calculates the angular velocity from the attitude angle derivative

[0011] The time of the deceleration phase

[0012]

[0013] θ0 and ψ0 are the three-axis attitudes of the starting point of the spacecraft's trajectory planning, is the attitude angle derivative of the starting point of the spacecraft's trajectory planning, seq is the attitude rotation sequence, a max is the maximum angular acceleration of the spacecraft.

[0014] Furthermore, controlling the spacecraft to maneuver an angle χ around the Euler axis Axis1 dw , specifically: when 0 ≤ t m ≤ t dw , calculate q at each moment r0 , ω r0 , and substitute them into the spacecraft control system, where:

[0015] t mdw =t m

[0016] t mdwsav =t mdw

[0017]

[0018] t mdw =t mdwsav -dt v

[0019]

[0020] t mdw =t mdwsav +dt Tr

[0021]

[0022] t mdw =t mdwsav

[0023] q r0 =[Axis1[1]·sin(χ r / 2), Axis1[2]sin(χ r / 2), Axis1[3]sin(χ r / 2), cos(χ r / 2)];

[0024]

[0025] t m is the time for trajectory planning;

[0026] χ r is the angle of rotation about the maneuvering axis for trajectory planning;

[0027] is the derivative of χ r ;

[0028] is the second derivative of χ r ;

[0029] t mdw 、t mdwsav are temporary variables;

[0030] dt v is the angular velocity lag parameter, determined according to the characteristics of the angular velocity sensor;

[0031] dt Tr is the angular acceleration lead parameter, determined according to the characteristics of the actuator;

[0032] q r0 is the quaternion from the starting point of attitude maneuver to the current moment for trajectory planning;

[0033] ω r0 is the angular velocity from the starting point of attitude maneuver to the current moment for trajectory planning.

[0034] Furthermore, in the acceleration phase, the spacecraft is controlled to maneuver an angle χ sw about the Euler axis Axis3 to achieve the acceleration of the spacecraft, where:

[0035]

[0036] nω sw = |ω sw |

[0037] Axis3 = [ω sw [1] / nω sw , ω sw [2] / nω sw , ω sw [3] / nω sw ​

[0038] Time of the acceleration phase

[0039]

[0040] θ m and ψ m are the end - point three - axis attitudes of the spacecraft's trajectory planning, and are the attitude angle derivatives at the end - point of the spacecraft's trajectory planning.

[0041] Furthermore, the control of the spacecraft to maneuver an angle χ around the Euler axis Axis3 sw , specifically: when t dw +t m3 ≤t m ≤t dw +t m3 +t sw calculate q rsa and ω rsa at each moment and substitute them into the spacecraft control system, where:

[0042] t msw =t m -t dw -t m3

[0043] t mswsav =t msw

[0044]

[0045] t msw =t mswsav -dt v

[0046]

[0047] t msw =t mdwsav +dt Tr

[0048]

[0049] t msw =t mswsav

[0050] q rsa =[Axis3[1]·sin(χ r / 2), Axis3[2]sin(χ r / 2), Axis3[3]sin(χ r / 2), cos(χ r / 2)];

[0051]

[0052] t m is the time for trajectory planning;

[0053] χ r is the angle of rotation about the maneuver axis for trajectory planning;

[0054] is the derivative of χ r ;

[0055] is the second derivative of χ r ;

[0056] t msw and t mswsav are temporary variables;

[0057] dt v is the angular velocity lag parameter, determined according to the characteristics of the angular velocity sensor;

[0058] dt Tr is the angular acceleration lead parameter, determined according to the characteristics of the actuator;

[0059] q rsa is the quaternion from the end time of the point-to-point maneuver segment to the current time for trajectory planning;

[0060] ω rsa is the angular velocity from the end time of the point-to-point maneuver segment to the current time for trajectory planning, [[ID=5`4]]

[0061] t m3 is the total time of the point-to-point maneuver segment.

[0062] Furthermore, the point-to-point maneuver segment is further divided into an inner acceleration segment, an inner constant velocity segment, and an inner deceleration segment, and the angular velocity is guaranteed to be 0 at the start and end points of the maneuver.

[0063] Furthermore, for the point-to-point maneuver segment, the spacecraft is controlled to maneuver an angle χ swdw about the Euler axis Axis2 to achieve the point-to-point maneuver of the spacecraft, where:

[0064]

[0065]

[0066] C mb0 = C mo C[[ID=7`9]] bo T

[0067] Cdw0 = q2DCM(q dw )

[0068] C msw = q2DCM(q sw )

[0069]

[0070]

[0071] C swdw = C msw T C mb0 C dw0 T

[0072] q swdw = DCM2q(C swdw )

[0073] χ swdw = 2·cos -1 (q swdw [4])

[0074] qv swdw = [q swdw [1], q swdw [2], q swdw [3]]

[0075] nqv swdw = |qv swdw |

[0076] Axis2 = [qv swdw [1] / nqv swdw , qv swdw [2] / nqv swdw , qv swdw [3] / nqv swdw

[0077] Angle2DCM is the calculation function from the attitude angle to the attitude matrix;

[0078] A T is the transpose of matrix A;

[0079] q2DCM is the calculation function from the quaternion to the attitude matrix;

[0080] DCM2q is the calculation function from the attitude matrix to the quaternion;

[0081] q swdw is the quaternion of the point-to-point maneuver segment;

[0082] q swdw[1], q swdw [2], q swdw [3] is the three components of the vector part of q swdw ;

[0083] q swdw [4] is the scalar part of q swdw ;

[0084] qv swdw is the vector part of q swdw ;

[0085] nqv swdw is the modulus of qv swdw ;

[0086] Furthermore, the durations of the inner acceleration section and the inner deceleration section are both t acc , and the duration of the inner constant velocity section is t v . First, let Then calculate If t v > 0, then the calculated t acc and t v are the actual durations; if t v ≤0, then t v = 0, where v max is the maximum angular velocity of the spacecraft.

[0087] Furthermore, controlling the spacecraft to maneuver an angle χ swdw around the Euler axis Axis2 specifically means: when t dw < t m ≤ t dw + t m3 , calculate q rp2p , ω rp2p at each moment and input them into the spacecraft control system,

[0088] t msa = t m - t dw , t msasav = t msa , t m1 = t acc , t m2 = t acc + t v , t m3 = 2·t acc + t v ,

[0089] When t msa ≥0 and t msa ≤ t m1 :

[0090]

[0091] When t msa ≥ t m1 and t msa ≤ t m2 then:

[0092]

[0093] When t msa ≥ t m2 and t msa ≤ t m3 then:

[0094]

[0095] t msa = t msasav - dt v

[0096] When t msa ≥ 0 and t msa ≤ t m1 then:

[0097]

[0098] When t msa ≥ t m1 and t msa ≤ t m2 then:

[0099]

[0100] When t msa ≥ t m2 and t msa ≤ t m3 then:

[0101]

[0102] t msa = t msasav + dt Tr

[0103] When t msa ≥ 0 and t msa ≤ t m1 then:

[0104]

[0105] When t msa ≥ t m1 and t msa ≤ t m2When:

[0106]

[0107] When t msa ≥t m2 and t msa ≤t m3 When:

[0108]

[0109] t msa =t msasav

[0110] q rp2p =[Axis2[1]·sin(χ r / 2), Axis2[2]sin(χ r / 2), Axis2[3]sin(χ r / 2), cos(χ r / 2)];

[0111]

[0112] where t msa and t msasav are temporary variables.

[0113] The advantages of the present invention compared with the prior art are as follows:

[0114] (1) Compared with the existing polynomial trajectory planning method, the present invention can automatically determine whether to execute the current attitude maneuver through the calculation result of the total maneuver time before the maneuver. The trajectory of the spacecraft during the maneuver is completely known in advance, realizing full control of the attitude maneuver process;

[0115] (2) By comparing with the existing polynomial trajectory planning method, it can be seen that in most working conditions, the maneuver time of the method of the present invention is shorter than that of the polynomial trajectory planning, realizing agile trajectory planning of the spacecraft. Brief Description of the Drawings

[0116] Figure 1 is the curve of the traditional polynomial trajectory planning method;

[0117] Figure 2 is the trajectory planning curve of the method of the present invention;

[0118] Figure 3 is the comparison between this method and the traditional polynomial trajectory planning, where 1 means the polynomial has a longer time and 0 means this method has a longer time. Detailed Embodiment

[0119] For active imaging, it is usually necessary for the spacecraft to maneuver from an arbitrary initial attitude and angular velocity to the desired attitude and angular velocity. Since the Euler axes of the angular velocity and the attitude angle may be different, it is necessary to first decelerate the initial angular velocity to 0, then perform a point-to-point maneuver for a specific angle, and finally accelerate the angular velocity to the desired angular velocity. Therefore, for any attitude maneuver, it can be decomposed into a deceleration section, a point-to-point maneuver section, and an acceleration section.

[0120] If the angular velocity of the initial satellite is 0, there is no deceleration section, only a point-to-point maneuver section and an acceleration section.

[0121] The main steps of the method of the present invention are as follows:

[0122] (1) Determine whether there is a deceleration section:

[0123] (1.1) Assume that during trajectory planning, the starting three-axis attitude θ0, ψ0, the starting attitude angle derivative the ending three-axis attitude θ m , ψ m , the ending three-axis attitude angle derivative attitude transformation sequence seq, the maximum angular velocity v of the spacecraft max , the maximum angular acceleration a max , all of these are known quantities;

[0124] (1.2) When the starting attitude angle derivative is not 0 during trajectory planning, the trajectory is divided into three sections: a deceleration section, a point-to-point maneuver section, and an acceleration section; when the starting attitude angle derivatives are all 0, the trajectory is divided into two sections: a point-to-point maneuver section and an acceleration section;

[0125] The attitude angle derivative is not 0, indicating that the satellite initially has an angular velocity. Therefore, it is necessary to first decelerate the angular velocity of the satellite to 0 through the deceleration section, and then perform the point-to-point maneuver and acceleration process.

[0126] (2) Calculate the maneuver time and angle for the two-section / three-section trajectory; if the maneuver time is insufficient, this mission is not executed:

[0127] (2.1) In the case of having a deceleration section, the deceleration time and maneuver angle of the deceleration section are:

[0128]

[0129] nω dw =|ω dw |

[0130] Axis1=[ω dw[1] / nω dw , ω dw [2] / nω dw , ω dw [3] / nω dw

[0131]

[0132]

[0133]

[0134] where ω dw is the angular velocity of the spacecraft at the starting point of trajectory planning;

[0135] dEuler2wbo() is the attitude kinematic function, which can calculate the angular velocity from the derivative of the attitude angle. For details, see Zhang Renwei, Satellite Orbit Attitude Dynamics and Control [M], Beijing University of Aeronautics and Astronautics Press, August 1998, Beijing;

[0136] nω dw is the modulus of the angular velocity of the spacecraft at the starting point of trajectory planning;

[0137] Axis1 is the Euler axis for attitude maneuver in the deceleration phase and is a three-dimensional vector;

[0138] Axis1[1], Axis1[2], Axis1[2] are the three-axis components of Axis1;

[0139] t dw is the time of the deceleration phase;

[0140] χ dw is the maneuver angle in the deceleration phase; the maneuver angle refers to the maneuver angle rotated around the Euler axis. According to the principle of rigid body dynamics, any attitude to another attitude can be described as completing a maneuver of an angle around an Euler axis.

[0141] q dw is the maneuver quaternion in the deceleration phase.

[0142] In the case of no deceleration phase, t dw = 0;

[0143] The subscript of the deceleration end point is dw, and the effect achieved in the deceleration phase is: reducing the angular velocity of the spacecraft to 0 and preparing for point-to-point maneuver.

[0144] (2.2) The maneuver time and maneuver angle in the acceleration phase are:

[0145]

[0146] nω sw ​= |ω sw |

[0147] Axis3 = [ω sw [1] / nω sw , ω sw [2] / nω sw , ω sw [3] / nω sw

[0148]

[0149]

[0150]

[0151] where ω sw is the angular velocity of the spacecraft at the end point of the trajectory planning;

[0152] nω sw is the magnitude of the angular velocity of the spacecraft at the end point of the trajectory planning;

[0153] Axis3 is the Euler axis in the acceleration phase;

[0154] Axis3[1], Axis3[2], Axis3[2] are the three-axis components of Axis3;

[0155] t sw is the time in the acceleration phase;

[0156] χ sw is the maneuvering angle in the acceleration phase;

[0157] q sw is the maneuvering quaternion in the acceleration phase.

[0158] The purpose of the acceleration phase itself is to accelerate from a stationary state to the desired three-axis attitude angle derivative while the attitude satisfies the desired three-axis attitude.

[0159] The subscript of the acceleration starting point is sw. In this step, the starting attitude of the acceleration phase is deduced from the desired attitude based on the maneuvering angle of the acceleration phase, preparing for calculating the parameters related to point-to-point maneuvers.

[0160] (2.3) The maneuvering angle in the point-to-point maneuver phase is:

[0161]

[0162]

[0163] C mb0 = C mo C bo T ​

[0164] C dw0 = q2DCM(q dw )

[0165] C msw = q2DCM(q sw )

[0166] C swdw = C msw T C mb0 C dw0 T

[0167] q swdw = DCM2q(C swdw )

[0168] χ swdw = 2·cos -1 (q swdw [4])

[0169] qv swdw = [q swdw [1], q swdw [2], q swdw [3]]

[0170] nqv swdw = |qv swdw |

[0171] Axis2 = [qv swdw [1] / nqv swdw , qv swdw [2] / nqv swdw , qv swdw [3] / nqv swdw

[0172] where C bo is the attitude matrix at the starting point of the attitude maneuver;

[0173] Angle2DCM is the calculation function from the attitude angle to the attitude matrix. For details, see Zhang Renwei, Satellite Orbit Attitude Dynamics and Control [M], Beihang University Press, Beijing, August 1998;

[0174] C mo is the attitude matrix at the ending point of the attitude maneuver;

[0175] C mb0 is the attitude matrix from the starting point to the ending point of the attitude maneuver;

[0176] A T is the transpose of matrix A, where matrix A can be any matrix;​

[0177] C dw0 is the attitude matrix from the starting point of the attitude maneuver to the ending point of the deceleration phase; if there is no deceleration phase, it is the identity matrix;

[0178] q2DCM is the calculation function from quaternion to attitude matrix;

[0179] DCM2q is the calculation function from attitude matrix to quaternion. For specific details, please refer to Zhang Renwei, Satellite Orbit Attitude Dynamics and Control [M], Beijing University of Aeronautics and Astronautics Press, August 1998, Beijing;

[0180] C msw is the attitude matrix from the starting point of the acceleration phase to the ending point of the attitude maneuver;

[0181] C swdw is the attitude matrix for the point-to-point maneuver segment;

[0182] q swdw is the quaternion for the point-to-point maneuver segment;

[0183] q swdw [1], q swdw [2], q swdw [3] are the three components of the vector part of q swdw ;

[0184] q swdw [4] is the scalar part of q swdw ;

[0185] χ swdw is the maneuvering angle for the point-to-point maneuver segment;

[0186] qv swdw is the vector part of q swdw ;

[0187] nqv swdw is the modulus of qv swdw ;

[0188] Axis2 is the Euler axis for the point-to-point maneuver segment;

[0189] The function of this step is to calculate parameters such as the maneuvering angle and Euler axis for the point-to-point maneuver, preparing for the final step of planning.

[0190] (2.4) The maneuvering time for the point-to-point maneuver segment is:

[0191]

[0192]

[0193] IF t v ≤0

[0194] t v = 0

[0195]

[0196] ENDIF

[0197] t m1 = t acc

[0198] t m2 = t acc + t v

[0199] t m3 = 2·t acc + t v

[0200] where t acc is the acceleration time of the point-to-point maneuver segment;

[0201] t v is the constant-speed time of the point-to-point maneuver segment;

[0202] t m1 is the same as t acc and is the acceleration time of the point-to-point maneuver segment;

[0203] t m2 is the sum of the acceleration time and the constant-speed time of the point-to-point maneuver segment;

[0204] t m3 is the total time of the point-to-point maneuver segment.

[0205] Here, the point-to-point maneuver can be further divided into an acceleration segment, a constant-speed segment, and a deceleration segment. The angular velocity is guaranteed to be 0 at both the start and end points of the maneuver. For details, see Fan Guowei, Wang Shaoju, Xu Wei, Chang Lin, Yang Xiubin, Wang Min, Three-stage Trajectory Planning and Rolling Tracking Control for Flexible Satellite Attitude Maneuver [J], Control Theory & Applications, 2018, 35(9), 1260 - 1271.

[0206] (2.5) The total time of the attitude maneuver is: t dw + t m3 + t sw . If the total time of the attitude maneuver is greater than the imaging start time minus the current time, then this task is not executed; if the total time of the attitude maneuver is less than the imaging start time minus the current time, then this task is executed.

[0207] (3) If there is a deceleration segment, conduct trajectory planning for the deceleration segment:

[0208] When 0 ≤ t m ≤ t dw :

[0209] t mdw = t m

[0210] t mdwsav = t mdw

[0211]

[0212] t mdw = t mdwsav -dt v

[0213]

[0214] t mdw = t mdwsav +dt Tr

[0215]

[0216] t mdw = t mdwsav

[0217] q r0 = [Axis1[1]·sin(χ r / 2), Axis1[2]sin(χ r / 2), Axis1[3]sin(χ r / 2), cos(χ r / 2)];

[0218]

[0219] where t m is the time of trajectory planning, starting from 0 and accumulating;

[0220] χ r is the angle of rotation about the maneuvering axis in trajectory planning;

[0221] is the derivative of χ r ;

[0222] is the second derivative of χ r ;

[0223] t mdw and t mdwsav are temporary variables;

[0224] dt v is the angular velocity lag parameter, determined according to the characteristics of the angular velocity sensor;

[0225] dt Tr It is the angular acceleration lead parameter, determined according to the characteristics of the actuator;

[0226] q r0 It is the quaternion from the starting point of the attitude maneuver in the trajectory planning to the current moment;

[0227] ω r0 It is the angular velocity from the starting point of the attitude maneuver in the trajectory planning to the current moment;

[0228] The basic principle of the formula is: first determine that the form of the acceleration is sinusoidal, and the integral can obtain the velocity planning formula, and then integrate to obtain the angle planning formula, and then determine the constant term according to the starting and ending states required in this paragraph.

[0229] The formula given in this paragraph is for the trajectory planning of the deceleration section. When 0 ≤ t m ≤ t dw In the time period, calculate q r0 , ω r0 at each moment according to the formula, and substitute it into the control system to realize the deceleration of the spacecraft. The Euler axis of the maneuver is Axis1, and the angle of maneuver around the Euler axis is χ r .

[0230] (4) Conduct trajectory planning for the point-to-point maneuver section:

[0231] When t dw <t m ≤ t dw + t m3 :

[0232] t msa =t m - t dw

[0233] t msasav =t msa

[0234] When t msa ≥ 0 and t msa ≤ t m1 :

[0235]

[0236] When t msa ≥ t m1 and t msa ≤ t m2 :

[0237]

[0238] When t msa ≥ t m2 and tmsa ≤t m3 When:

[0239]

[0240] t msa = t msasav - dt v

[0241] When t msa ≥ 0 and t msa ≤ t m1 When:

[0242]

[0243] When t msa ≥ t m1 and t msa ≤ t m2 When:

[0244]

[0245] When t msa ≥ t m2 and t msa ≤ t m3 When:

[0246]

[0247] t msa = t msasav + dt Tr

[0248] When t msa ≥ 0 and t msa ≤ t m1 When:

[0249]

[0250] When t msa ≥ t m1 and t msa ≤ t m2 When:

[0251]

[0252] When t msa ≥ t m2 and t msa ≤ t m3 When:

[0253]

[0254] t msa = t msasav

[0255] q rp2p = [Axis2[1]·sin(χ r / 2), Axis2[2]sin(χ r / 2), Axis2[3]sin(χ r / 2), cos(χ r / 2)];

[0256]

[0257] where t msa , t msasav are temporary variables;

[0258] q rp2p is the quaternion from the end time of the deceleration phase to the current time for trajectory planning;

[0259] ω rp2p is the angular velocity from the end time of the deceleration phase to the current time for trajectory planning;

[0260] The formula for trajectory planning in the point-to-point maneuver phase is given. In the time period when t dw < t m ≤ t dw + t m3 , calculate q rp2p , ω rp2p at each moment according to the formula and substitute them into the control system to achieve the maneuver of the spacecraft. The Euler axis of the maneuver is Axis2, and the angle of rotation around the Euler axis is χ r .

[0261] (5) Perform trajectory planning for the acceleration phase:

[0262] When t dw + t m3 ≤ t m ≤ t dw + t m3 + t sw :

[0263] t msw = t m - t dw - t m3

[0264] t mswsav = t msw

[0265]

[0266] t msw = t mswsav - dtv

[0267]

[0268] t msw = t mdwsav + dt Tr

[0269]

[0270] t msw = t mswsav

[0271] q rsa = [Axis3[1]·sin(χ r [[ID=XX]] / 2), Axis3[2]sin(χ r [[ID=XX]] / 2), Axis3[3]sin(χ r [[ID=XX]] / 2), cos(χ r / 2)];

[0272]

[0273] where t msw 、t mswsav are temporary variables;

[0274] q rsa is the quaternion from the end time of the point-to-point maneuver segment to the current time of the trajectory planning; s

[0275] ω rsa is the angular velocity from the end time of the point-to-point maneuver segment to the current time of the trajectory planning.

[0276] The formulas for the trajectory planning of the point-to-point maneuver segment are given in this section. In the time period of t dw + t m3 ≤ t m ≤ t dw + t m3 + t sw calculate q rsa and ω rsa at each moment according to the formulas, and substitute them into the control system to achieve the maneuver of the spacecraft. The Euler axis of the maneuver is Axis3, and the angle of rotation around the Euler axis is χ r .

[0277] Finally, the agile and safe trajectory planning of the spacecraft is completed.

[0278] Embodiment

[0279] The starting three-axis attitude of the trajectory planning θ0 = 0, ψ0 = 0, the derivative of the starting attitude angle Note: There seems to be some incorrect or incomplete expressions in the original text, such as "Axis3[2]sin(χ and "Axis3[3]sin(χ which are likely missing operators. I have translated them as best as possible while maintaining the original structure. Final three-axis attitude θ m = 0, ψ m = 0, the derivative of the final three-axis attitude angle Attitude rotation sequence seq = 123, the maximum angular velocity v of the spacecraft max = 2.0 deg / s, the maximum angular acceleration a max = 0.5 deg / s.

[0280] For this embodiment, when the derivatives of the starting attitude angles of the trajectory planning are all 0, the trajectory is divided into two segments: the point-to-point maneuver segment and the acceleration segment.

[0281] Figure 1 It is a polynomial trajectory planning curve. As can be seen from the figure, the time required for polynomial planning is 56 seconds.

[0282] Figure 2 It is the trajectory planning curve of the method of the present invention. As can be seen from the figure, the time required for the present invention is 37.75 seconds.

[0283] Figure 3 This is the comparison between the method of the present invention and the existing polynomial trajectory planning. Among them, 1 means that the polynomial time is longer, and 0 means that the time of this method is longer. Through statistics, the time required for maneuvering in 80% of the working conditions of this method is shorter than that of polynomial planning, realizing the agile and safe trajectory planning of the spacecraft.

[0284] The content not described in detail in the specification of the present invention belongs to the well-known technology of those skilled in the art.

Claims

1. An agile and safe segmented trajectory planning method for a spacecraft, characterized in that: According to whether the three-axis attitude angular velocity of the spacecraft at the starting point of trajectory planning is 0, the spacecraft motion trajectory is planned in two segments or three segments. If the three-axis attitude angular velocity of the spacecraft at the starting point of trajectory planning is 0, the spacecraft motion trajectory is planned in two segments with a point-to-point maneuver segment and an acceleration segment. If the three-axis attitude angular velocity of the spacecraft at the starting point of trajectory planning is not 0, the spacecraft motion trajectory is planned in three segments with a deceleration segment, a point-to-point maneuver segment, and an acceleration segment.

2. The method for agile and safe segmented trajectory planning of a spacecraft according to claim 1, wherein: In the deceleration stage, control the maneuvering angle χ of the spacecraft around the Euler axis Axis1 dw , to achieve deceleration of the spacecraft, where: Axis1 = [ω dw [1] / nω dw , ω dw [2] / nω dw , ω dw [3] / nω dw ​ nω dw = |ω dw | dEuler2wbo() is an attitude kinematic function that calculates the angular velocity from the derivative of the attitude angle Time of the deceleration section θ0 and ψ0 are the three-axis attitudes at the starting point of the spacecraft's trajectory planning, is the attitude angular derivative at the starting point of the spacecraft's trajectory planning, seq is the attitude rotation sequence, a max is the maximum angular acceleration of the spacecraft; ω dw The angular velocity of the spacecraft at the starting point of trajectory planning; nω dw The magnitude of the angular velocity of the spacecraft at the starting point of trajectory planning.

3. The method for agile and safe segmented trajectory planning of a spacecraft according to claim 2, characterized in that: The maneuvering angle χ of the control spacecraft around the Euler axis Axis1 dw is specifically as follows: when 0 ≤ t m ≤ t dw , calculate q r0 , ω r0 at each moment and substitute them into the spacecraft control system, where: t mdw = t m t mdwsav = t mdw t mdw = t mdwsav -dt v t mdw = t mdwsav + dt Tr t mdw = t mdwsav q r0 = [Axis1[1]·sin(χ r / 2), Axis1[2]sin(χ r / 2), Axis1[3]sin(χ r / 2), cos(χ r / 2)]; t m Time for trajectory planning; χ r The angle of rotation about the maneuvering axis for trajectory planning; is the derivative of χ r ; is the second derivative of χ r ; t mdw 、t mdwsav are temporary variables; dt v is the angular velocity lag parameter, which is determined according to the characteristics of the angular velocity sensor; dt Tr It is the angular acceleration lead parameter, which is determined according to the characteristics of the actuator; q r0 The quaternion from the starting point of the slave attitude maneuver for trajectory planning to the current moment; ω r0 is the angular velocity from the starting point of the slave attitude maneuver for trajectory planning to the current moment; Axis1[1], Axis1[2], and Axis1[3] are the three-axis components of Axis1.

4. A method for agile and safe segmented trajectory planning of a spacecraft according to claim 2, characterized in that: In the acceleration stage, control the maneuvering angle χ of the spacecraft around the Euler axis Axis3 sw , to achieve the acceleration of the spacecraft, where: nω sw = |ω sw | Axis3 = [ω sw [1] / nω sw , ω sw [2] / nω sw , ω sw [3] / nω sw ​ Time of the acceleration section θ m 、ψ m are the three-axis attitudes at the end point of the trajectory planning of the spacecraft, and are the attitude angle derivatives at the end point of the trajectory planning of the spacecraft; ω sw The angular velocity of the spacecraft at the end point of trajectory planning; nω sw The magnitude of the angular velocity of the spacecraft at the end point of the trajectory planning.

5. The agile and safe segmented trajectory planning method for a spacecraft according to claim 4, wherein: The maneuvering angle χ of the spacecraft around the Euler axis Axis3 mentioned above sw , specifically: when t dw +t m3 ≤t m ≤t dw +t m3 +t sw , calculate q rsa , ω rsa at each moment and substitute them into the spacecraft control system, where: t msw = t m -t dw -t m3 t mswsav = t msw t msw = t mswsav - dt v t msw = t mdwsav + dt Tr t msw = t mswsav q rsa = [Axis3[1]·sin(χ r / 2), Axis3[2]sin(χ r / 2), Axis3[3]sin(χ r / 2), cos(χ r / 2)]; t m Time for trajectory planning; χ r The angle of rotation about the maneuvering axis for trajectory planning; is the derivative of χ r ; is the second derivative of χ r ; t msw 、t mswsav are temporary variables; dt v is the angular velocity lag parameter, which is determined according to the characteristics of the angular velocity sensor; dt Tr It is the angular acceleration lead parameter, which is determined according to the characteristics of the actuator; q rsa The quaternion from the end time of the point-to-point maneuver segment of the trajectory planning to the current time; ω rsa is the angular velocity from the end time of the point-to-point maneuver segment of the trajectory planning to the current time t m3 is the total time of the point-to-point maneuvering section.

6. A method for agile and safe segmented trajectory planning of a spacecraft according to claim 4, characterized in that: The point-to-point maneuver segment is further divided into an inner acceleration segment, an inner constant velocity segment, and an inner deceleration segment, and the angular velocity is ensured to be 0 at both the start and end points of the maneuver.

7. A method for agile and safe segmented trajectory planning of a spacecraft according to claim 6, characterized in that: For the described point-to-point maneuvering section, control the spacecraft to maneuver by an angle χ around the Euler axis Axis2 swdw , to achieve the point-to-point maneuvering of the spacecraft, where: C mb0 = C mo C bo T C dw0 = q2DCM(q dw ) C msw = q2DCM(q sw ) C swdw = C msw T C mb0 C dw0 T q swdw = DCM2q(C swdw ) χ swdw = 2·cos -1 (q swdw [4]) qv swdw = [q swdw [1], q swdw [2], q swdw [3]] nqv swdw = |qv swdw | Axis2 = [qv swdw [1] / nqv swdw ,qv swdw [2] / nqv swdw ,qv swdw [3] / nqv swdw ​ Angle2DCM is a calculation function from the attitude angle to the attitude matrix; A T is the transpose of matrix A; q2DCM is a calculation function from the quaternion to the attitude matrix; DCM2q is a calculation function from the attitude matrix to the quaternion; q swdw is the quaternion for the point-to-point maneuvering section; q swdw [1], q swdw [2], q swdw [3] is q swdw The three components of the vector part of q swdw [4] is the scalar part of q swdw ; qv swdw is the vector part of q swdw ; nqv swdw is the modulus of qv swdw ; C bo The attitude matrix that is the starting point of the attitude maneuver; C mo The attitude matrix at the end of the attitude maneuver; C mb0 is the attitude matrix from the starting point to the ending point of the attitude maneuver; C dw0 is the attitude matrix from the starting point of attitude maneuver to the ending point of the deceleration section, or the identity matrix if there is no deceleration section; C msw is the attitude matrix from the starting point of the acceleration section to the ending point of attitude maneuver; q dw The maneuver quaternion for the deceleration phase; q sw The quaternion of maneuver for the acceleration phase; Axis1[1], Axis1[2], and Axis1[3] are the three-axis components of Axis1; Axis3 is the Euler axis of the acceleration section; Axis3[1], Axis3[2], Axis3[2] are the three-axis components of Axis3; χ sw is the maneuvering angle of the acceleration section; C swdw is the attitude matrix for the point-to-point maneuvering section; χ swdw is the angle of maneuver in the point-to-point maneuvering section.

8. A method for agile and safe segmented trajectory planning of a spacecraft according to claim 7, characterized in that: The durations of the inner acceleration section and the inner deceleration section are both t acc The duration of the inner constant speed section is t v First, let Then calculate If t v > 0, then the calculated t acc and t v are the actual durations; If t v ≤ 0, then t v = 0, where v max is the maximum angular velocity of the spacecraft.

9. A method for agile and safe segmented trajectory planning of a spacecraft according to claim 8, characterized in that: The maneuvering angle χ of the spacecraft around the Euler axis Axis2 mentioned above swdw , specifically: when t dw < t m ≤ t dw + t m3 , calculate q rp2p , ω rp2p at each moment and input them into the spacecraft control system t msa = t m - t dw ,t msasav = t msa ,t m1 = t acc ,t m2 = t acc + t v ,t m3 = 2·t acc + t v , When t msa ≥ 0 and t msa ≤ t m1 : When t msa ≥ t m1 and t msa ≤ t m2 then: When t msa ≥ t m2 and t msa ≤ t m3 then: t msa = t msasav -dt v When t msa ≥ 0 and t msa ≤ t m1 : When t msa ≥ t m1 and t msa ≤ t m2 then: When t msa ≥ t m2 and t msa ≤ t m3 then: t msa = t msasav + dt Tr When t msa ≥ 0 and t msa ≤ t m1 : When t msa ≥ t m1 and t msa ≤ t m2 : When t msa ≥ t m2 and t msa ≤ t m3 then: t msa = t msasav q rp2p = [Axis2[1]·sin(χ r / 2), Axis2[2]sin(χ r / 2), Axis2[3]sin(χ r / 2), cos(χ r / 2)]; where t msa and t msasav are temporary variables; q rp2p The quaternion from the end time of the deceleration phase to the current time for trajectory planning; ω rp2p is the angular velocity from the end time of the deceleration segment to the current time for trajectory planning; dt v is the angular velocity lag parameter, which is determined according to the characteristics of the angular velocity sensor; dt Tr It is the angular acceleration lead parameter, which is determined according to the characteristics of the actuator; χ r The angle of rotation about the maneuvering axis for trajectory planning; is the derivative of χ r ; is the second derivative of χ r ; t m Time for trajectory planning; t m1 is the acceleration time of the point-to-point maneuvering section; t m2 is the sum of the acceleration time and the constant-speed time of the point-to-point maneuvering section; t m3 is the total time of the point-to-point maneuvering section; Axis2[1], Axis2[2], and Axis2[3] are the three-axis components of Axis2.

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