Geometric analysis-based spacecraft attitude maneuver pointing constraint path planning method

Abstract

The invention provides a spacecraft attitude maneuver pointing constraint path planning method based on geometric analysis, and belongs to the technical field of spacecraft attitude maneuver, and the method comprises the steps: calculating an attitude maneuver path quaternion sequence under non-pointing constraint; judging whether the sequence meets a pointing constraint condition or not; if not, calculating two critical attitude quaternions meeting the constraint, and planning a maneuvering path between the two critical attitude quaternions; and combining the quaternion sequences of all sections of paths to form a complete attitude maneuver path meeting the pointing constraint. According to the method, the feasible path is directly constructed through geometric analysis, the problems that a traditional optimization method is large in calculation amount and prone to falling into local optimum are solved, and the reliability and efficiency of path planning are improved.

Description

Technical Field

[0001] This invention relates to the field of spacecraft attitude maneuvering technology, and more specifically, to a spacecraft attitude maneuvering pointing constraint path planning method based on geometric analysis. Background Technology

[0002] The missions and functions of modern spacecraft platforms are becoming increasingly diverse and demanding, placing ever higher requirements on their agile maneuverability. During on-orbit operation, spacecraft frequently need to perform large-angle attitude maneuvers to complete various space missions. However, during these maneuvers, the performance of certain optical sensors is susceptible to stray light interference or damage; this constraint is often referred to as pointing constraint during spacecraft attitude maneuvers. Research on spacecraft attitude maneuver path planning considering pointing constraints has significant engineering application value.

[0003] Currently, commonly used spacecraft attitude maneuver planning methods under pointing constraints generally transform the constraints into a mathematical optimization problem, and then use gradient descent or particle swarm optimization algorithms to optimize and solve this problem. This method has a large computational load and may not have a solution. For example, the spacecraft attitude maneuver planning method described in the paper: Yue Chengfei, Lu Ming, Wu Fan, Huo Tao, Chen Xueqin. Efficient maneuver path planning and time-domain adjustment method for spacecraft under complex constraints [J]. Journal of National University of Defense Technology, 2024, 46(4): 63-73. adopts the gradient descent method to optimize the constraint problem. However, the gradient descent method may get stuck in local minima, which may lead to the failure of attitude planning. Summary of the Invention

[0004] To address the shortcomings of existing technologies, the purpose of this invention is to provide a spacecraft attitude maneuvering pointing constraint path planning method based on geometric analysis.

[0005] A spacecraft attitude maneuvering pointing constraint path planning method based on geometric analysis, provided by the present invention, includes: Step S1: Calculate the quaternion sequence for spacecraft attitude maneuvering path planning without direction constraints; Step S2: Determine whether the quaternion sequence of spacecraft attitude maneuver path planning under no-pointing constraint satisfies the spacecraft pointing constraint; if all are satisfied, the entire attitude planning is completed; otherwise, proceed to step S3. Step S3: Calculate the sequence of quaternions for maneuver path planning between two critical attitude quaternions of the spacecraft under pointing constraints; Step S4: Combine the quaternion sequences from the above steps to obtain the quaternion sequence for spacecraft attitude maneuvering path planning under pointing constraints.

[0006] Preferably, step S1 includes the following sub-steps: Step S101: Calculate the quaternion from the spacecraft's current attitude to the target attitude:

[0007] in, The quaternion representing the spacecraft's current attitude to its target attitude. The quaternion represents the target attitude of the spacecraft. Indicates the spacecraft's current attitude; Step S102: Calculate the spacecraft's attitude quaternion from the current moment. Quaternion of spacecraft target attitude Euler angles that need to be rotated and rotational Euler vector :

[0008]

[0009] in, express The scalar part, , , They represent The first, second, and third components of the vector part; Step S103: Based on the number of planned quaternion sequences as well as Calculate the quaternion sequence for spacecraft attitude maneuvering path planning without direction constraints: ( (This represents the quaternion sequence index) based on ( ),calculate as well as :

[0010] Among them, the attitude transformation matrix Quaternions It was converted from.

[0011] Preferably, in step S2, it is determined whether the quaternion sequence of spacecraft attitude maneuvering path planning under no-pointing constraints completely satisfies the spacecraft pointing constraints: The spacecraft attitude maneuvering pointing constraint is determined as follows:

[0012] in, This represents a vector in the spacecraft's body coordinate system. This represents a vector in the J2000 inertial frame. Let the attitude transformation matrix be the matrix from the J2000 inertial frame to the home frame. If for all... All have If the quaternion sequence of the spacecraft attitude maneuver path planning under no-pointing constraint satisfies the spacecraft pointing constraint, then the entire attitude planning is complete; otherwise, proceed to step S3.

[0013] Preferably, step S3 includes the following sub-steps: Step S301: According to Record the values ​​in ascending order of size. of and store in an array In the middle, let array The length is , , These are two critical quaternions that satisfy the pointing constraints, where... , Representing arrays respectively The first number and the last number; Step S302: Calculate the quaternion that satisfies the pointing constraint. To quaternions The sequence of quaternions between them: Note Will The vector projected onto this system is ,use Will The vector projected onto this system is ,Depend on , The unit vector of the plane normal and the vector formed by , The unit vectors of the plane normals formed are as follows:

[0014]

[0015] Calculate quaternions To quaternions Euler angles that need to be rotated :

[0016] Calculate quaternions To quaternions Rotation Euler vector Direction symbol : like ,So ,otherwise ; in Quaternion The result is obtained by converting it into an attitude transformation matrix. Quaternion The result is obtained by converting it into an attitude transformation matrix, denoted as... ; According to quaternions To quaternions The length of the quaternion sequence between planning The resulting sequence of quaternions is: ( ) Calculate quaternions To quaternions Euler angles that need to be rotated :

[0017] Step S303: Calculate the quaternion To quaternions Euler angles that need to be rotated and rotational Euler vector :

[0018]

[0019]

[0020] in, express The scalar part, , , They represent The first, second, and third components of the vector part According to quaternions To quaternions The length of the quaternion sequence between planning This yields the sequence of quaternions for planning: ( ) Preferably, step S4 includes: Determine whether the quaternion sequence for spacecraft attitude maneuvering path planning without direction constraints satisfies the direction constraint. If it does, then... ( This is the required quaternion sequence for path planning; otherwise, construct the following combined quaternion sequence. , This is the required quaternion sequence for path planning:

[0021] in , , , .

[0022] A spacecraft attitude maneuvering pointing constraint path planning system based on geometric analysis, according to the present invention, includes: Module M1: Calculates the quaternion sequence for spacecraft attitude maneuvering path planning without direction constraints; Module M2: Determines whether the quaternion sequence for spacecraft attitude maneuvering path planning under no-pointing constraints fully satisfies the spacecraft pointing constraints; if fully satisfied, the entire attitude planning is complete; otherwise, proceed to Module M3. Module M3: Calculates the sequence of quaternions for maneuver path planning between two critical attitude quaternions of a spacecraft under pointing constraints; Module M4: Combines the quaternion sequences from the above steps to obtain the quaternion sequence for spacecraft attitude maneuvering path planning under pointing constraints.

[0023] Preferably, module M1 includes the following sub-modules: Module M101: Calculates the quaternion from the spacecraft's current attitude to its target attitude.

[0024] in The quaternion represents the target attitude of the spacecraft. Indicates the spacecraft's current attitude; Module M102: Calculates the spacecraft's attitude quaternion at the current moment. Quaternion of spacecraft target attitude Euler angles that need to be rotated and rotational Euler vector :

[0025]

[0026] in, express The scalar part, , , They represent The first, second, and third components of the vector part; Module M103: Based on the number of quaternion sequences planned as well as Calculate the quaternion sequence for spacecraft attitude maneuvering path planning without direction constraints: ( ) based on ( ),calculate as well as :

[0027] Among them, the attitude transformation matrix Quaternions It was converted from.

[0028] Preferably, module M2 includes: The spacecraft attitude maneuvering pointing constraint is determined as follows:

[0029] in, This represents a vector in the spacecraft's body coordinate system. This represents a vector in the J2000 inertial frame. Let the attitude transformation matrix be the matrix from the J2000 inertial frame to the home frame. If for all... All have If the quaternion sequence of the spacecraft attitude maneuver path planning under no-pointing constraint satisfies the spacecraft pointing constraint, then the entire attitude planning is complete; otherwise, proceed to module M3.

[0030] Preferably, module M3 includes the following sub-modules: Module M301: According to Record the values ​​in ascending order of size. of and store in an array In the middle, let array The length is , , These are two critical quaternions that satisfy the pointing constraints; Module M302: Calculates quaternions that satisfy pointing constraints To quaternions The sequence of quaternions between them: Note Will The vector projected onto this system is ,use Will The vector projected onto this system is ,Depend on , The unit vector of the plane normal and the vector formed by , The unit vectors of the plane normals formed are as follows:

[0031]

[0032] Calculate quaternions To quaternions Euler angles that need to be rotated :

[0033] Calculate quaternions To quaternions Rotation Euler vector Direction symbol : like ,So ,otherwise ; in Quaternion The result is obtained by converting it into an attitude transformation matrix. Quaternion The result is obtained by converting it into an attitude transformation matrix, denoted as... ; According to quaternions To quaternions The length of the quaternion sequence between planning The resulting sequence of quaternions is: ( ) Calculate quaternions To quaternions Euler angles that need to be rotated :

[0034] Module M303: Calculate Quaternions To quaternions Euler angles that need to be rotated and rotational Euler vector :

[0035]

[0036]

[0037] According to quaternions To quaternions The length of the quaternion sequence between planning This yields the sequence of quaternions for planning: ( ) Preferably, the module M4 includes: Determine whether the quaternion sequence for spacecraft attitude maneuvering path planning without direction constraints satisfies the direction constraint. If it does, then... ( This is the required quaternion sequence for path planning; otherwise, construct the following combined quaternion sequence. , This is the required quaternion sequence for path planning:

[0038] in , , , .

[0039] Compared with the prior art, the present invention has the following beneficial effects: 1. This invention directly calculates the critical quaternion and path sequence that satisfy the pointing constraint through geometric analysis, avoiding the complex mathematical optimization process (such as gradient descent and particle swarm optimization) in traditional methods, significantly reducing the computational burden and improving the real-time performance and reliability of path planning.

[0040] 2. Traditional optimization methods are prone to getting trapped in local minima, leading to planning failure. However, this invention directly constructs feasible paths based on geometric structures, ensuring that feasible attitude maneuver paths can still be effectively generated under pointing constraints, thus improving the success rate and stability of planning. Attached Figure Description

[0041] Other features, objects, and advantages of the present invention will become more apparent from the following detailed description of non-limiting embodiments with reference to the accompanying drawings: Figure 1 This is a flowchart of the spacecraft attitude maneuvering pointing constraint path planning method based on geometric analysis in an embodiment of the present invention; Figure 2 This is the attitude quaternion planning case under pointing constraints in the embodiments of the present invention; Figure 3 This is a schematic diagram of the pointing constraint angle in an embodiment of the present invention. Detailed Implementation

[0042] The present invention will now be described in detail with reference to specific embodiments. These embodiments will help those skilled in the art to further understand the present invention, but do not limit the invention in any way. It should be noted that those skilled in the art can make several changes and improvements without departing from the concept of the present invention. These all fall within the protection scope of the present invention.

[0043] This invention provides a spacecraft attitude maneuvering pointing constraint path planning method based on geometric analysis. The method utilizes the target attitude quaternion, the current spacecraft attitude quaternion, and pointing constraint information to achieve spacecraft attitude maneuvering path planning. Specifically, it includes: S1. Calculate the quaternion sequence for spacecraft attitude maneuvering path planning under undirected constraints; S2. Determine whether the quaternion sequence of spacecraft attitude maneuvering path planning under no pointing constraints fully satisfies the spacecraft pointing constraints. S3. Calculate the sequence of quaternions for maneuver path planning between two critical attitude quaternions of a spacecraft under pointing constraints. S4. Combine the quaternion sequences from the above steps to obtain the quaternion sequence for spacecraft attitude maneuvering path planning under pointing constraints.

[0044] In S1, the process of calculating the quaternion sequence for spacecraft attitude maneuvering path planning without direction constraints is as follows: S101: Calculate the quaternion from the spacecraft's current attitude to the target attitude:

[0045] in The quaternion represents the target attitude of the spacecraft. Indicates the spacecraft's current attitude; S102: Based on the quaternion of the spacecraft's current attitude. Quaternion of spacecraft target attitude Euler angles that need to be rotated and rotational Euler vector :

[0046]

[0047] in, , , , They represent The scalar part and the first, second, and third components of the vector part.

[0048] S103: Based on the number of quaternion sequences planned. as well as Calculate the quaternion sequence for spacecraft attitude maneuvering path planning without direction constraints: ( ) based on ( ),calculate as well as :

[0049] Among them, the attitude transformation matrix Quaternions It was converted from.

[0050] In S2, it is determined whether the quaternion sequence of spacecraft attitude maneuvering path planning under no-direction constraint completely satisfies the spacecraft pointing constraint: The spacecraft attitude maneuvering pointing constraint is determined as follows:

[0051] in, It represents a vector in the spacecraft's body coordinate system (generally, it can be the sensor's optical axis vector). This represents a vector in the J2000 inertial frame (usually the position vector of the sun or moon). Let the attitude transformation matrix from the J2000 inertial frame to the home frame be denoted as . Therefore, the above formula represents the vector of the spacecraft during attitude maneuvers. With vector The included angle Needs to be greater than the angle .

[0052] If for all All have If the quaternion sequence of the spacecraft attitude maneuver path planning under no-direction constraint satisfies the spacecraft direction constraint, then the entire attitude planning is complete; otherwise, proceed to S3.

[0053] In S3, the process of calculating the maneuver path planning quaternion sequence between two critical attitude quaternions of the spacecraft under pointing constraints is as follows: S301: According to Record the values ​​in ascending order of size. of and store in an array In the middle, let array The length is ,So , These are two critical quaternions that satisfy the pointing constraints.

[0054] S302: Calculate quaternions that satisfy the pointing constraints. To quaternions The sequence of quaternions between them: Note Will The vector projected onto this system is ,use Will The vector projected onto this system is , then by , The unit vector of the plane normal and the vector formed by , The unit vectors of the plane normals formed are as follows:

[0055]

[0056] Calculate quaternions To quaternions Euler angles that need to be rotated :

[0057] Calculate quaternions To quaternions Rotation Euler vector Direction symbol : like ,So ,otherwise .

[0058] in Quaternion The result is obtained by converting it into an attitude transformation matrix. Quaternion The result is obtained by converting it into an attitude transformation matrix, denoted as...

[0059] According to quaternions To quaternions The length of the quaternion sequence between planning This yields the sequence of quaternions for planning: ( ) Calculate quaternions To quaternions Euler angles that need to be rotated :

[0060] S303: Calculate quaternions To quaternions Euler angles that need to be rotated and rotational Euler vector :

[0061]

[0062]

[0063] According to quaternions To quaternions The length of the quaternion sequence between planning This yields the sequence of quaternions for planning: ( ) In S4, the process of combining the quaternion sequences of S1, S2, and S3 to obtain the quaternion sequence for spacecraft attitude maneuvering path planning under pointing constraints is as follows: Determine whether the quaternion sequence for spacecraft attitude maneuvering path planning without direction constraints satisfies the direction constraint. If it does, then... ( This is the required quaternion sequence for path planning; otherwise, construct the following combined quaternion sequence. , This is the required quaternion sequence for path planning:

[0064] in , , , .

[0065] The present invention also provides a spacecraft attitude maneuvering pointing constraint path planning system based on geometric analysis. The spacecraft attitude maneuvering pointing constraint path planning system based on geometric analysis can be implemented by executing the process steps of the spacecraft attitude maneuvering pointing constraint path planning method based on geometric analysis. That is, those skilled in the art can understand the spacecraft attitude maneuvering pointing constraint path planning method based on geometric analysis as a preferred embodiment of the spacecraft attitude maneuvering pointing constraint path planning system based on geometric analysis.

[0066] A spacecraft attitude maneuvering pointing constraint path planning system based on geometric analysis, according to the present invention, includes: Module M1: Calculates the quaternion sequence for spacecraft attitude maneuvering path planning without direction constraints; Module M2: Determines whether the quaternion sequence for spacecraft attitude maneuvering path planning under no-pointing constraints fully satisfies the spacecraft pointing constraints; if fully satisfied, the entire attitude planning is complete; otherwise, proceed to Module M3. Module M3: Calculates the sequence of quaternions for maneuver path planning between two critical attitude quaternions of a spacecraft under pointing constraints; Module M4: Combines the quaternion sequences from the above steps to obtain the quaternion sequence for spacecraft attitude maneuvering path planning under pointing constraints.

[0067] Those skilled in the art will understand that, besides implementing the system and its various devices, modules, and units provided by this invention in the form of purely computer-readable program code, the same functions can be achieved entirely through logical programming of the method steps, enabling the system and its various devices, modules, and units to function in the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers, and embedded microcontrollers. Therefore, the system and its various devices, modules, and units provided by this invention can be considered a hardware component, and the devices, modules, and units included therein for implementing various functions can also be considered structures within the hardware component; alternatively, the devices, modules, and units for implementing various functions can be considered both software modules implementing the method and structures within the hardware component.

[0068] Specific embodiments of the present invention have been described above. It should be understood that the present invention is not limited to the specific embodiments described above, and those skilled in the art can make various changes or modifications within the scope of the claims, which do not affect the essence of the present invention. Unless otherwise specified, the embodiments and features described in this application can be arbitrarily combined with each other.

Claims

1. A geometric analysis based spacecraft attitude maneuver pointing constraint path planning method, characterized in that, The method comprises the following steps: Step S1: calculating a quaternion sequence of a spacecraft attitude maneuver path planning without a pointing constraint; Step S2: judging whether the quaternion sequence of the spacecraft attitude maneuver path planning without the pointing constraint satisfies a spacecraft pointing constraint; if yes, the whole attitude planning is completed, otherwise, entering step S3; Step S3: calculating a quaternion sequence of a spacecraft attitude maneuver path planning between two critical attitude quaternions with the pointing constraint; Step S4: combining the quaternion sequences of the above steps to obtain a quaternion sequence of the spacecraft attitude maneuver path planning with the pointing constraint.

2. The geometric analysis based spacecraft attitude maneuver pointing constraint path planning method of claim 1, wherein, The step S1 comprises the following sub-steps: Step S101: calculating a quaternion from a current attitude of the spacecraft to a target attitude; wherein, denotes the quaternion of the spacecraft's current time attitude to the target attitude, denotes the target attitude quaternion of the spacecraft, denotes the spacecraft's current time attitude; Step S102: Calculate the Euler angles that the spacecraft needs to turn through from the current time attitude quaternion to the spacecraft target attitude quaternion and the rotation Euler vector : wherein denotes the scalar part of , , denote the first component, the second component, the third component of the vector part, respectively. Step S103: Calculate the number of planned quaternion sequences And Calculate the spacecraft attitude maneuver path planning quaternion sequence without pointing constraints: ( , denotes quaternion sequence index) based on ( ),calculate as well as : where the pose transformation matrix is derived from the quaternion conversion.

3. The geometric analysis based spacecraft attitude maneuver pointing constraint path planning method according to claim 1, wherein, In the step S2, whether the quaternion sequence of the spacecraft attitude maneuver path planning without the pointing constraint satisfies the spacecraft pointing constraint is judged. The spacecraft attitude maneuver pointing constraint is judged as: wherein, represents a vector in the spacecraft body coordinate system, represents a vector in the J2000 inertial system, represents the attitude transformation matrix from the spacecraft J2000 inertial system to the body system, and if for all , all have then the spacecraft attitude maneuver path planning quaternion sequence under the non-directional constraint all satisfy the spacecraft directional constraint, and in this case the entire attitude planning is completed, otherwise step S3 is entered.

4. The geometric analysis based spacecraft attitude maneuver pointing constraint path planning method of claim 1, wherein, The step S3 comprises the following sub-steps: Step S301: According to from small to large order, record in turn satisfying , and store in array , record the length of array , , respectively as two critical quaternions satisfying the pointing constraint, wherein , respectively represent the first number, the last number of array ; Step S302: Calculate quaternions that satisfy the pointing constraint to quaternions between the planning quaternion sequence: Record with Will The vector projected onto the body system is , with Will The vector projected onto the body system is , by , The unit vector of the normal plane and the unit vector of the normal plane composed of , Respectively: Computing quaternions To quaternion Euler angles to turn : Computing quaternions To quaternions Rotation Euler vector Sign of direction : if , then , else ; wherein is a quaternion is converted into a pose transformation matrix to obtain is a quaternion is converted into a pose transformation matrix to obtain, denoted by ; According to the quaternion to the quaternion planned quaternion sequence length , a planned quaternion sequence is obtained （ ） Computing quaternions To quaternions Euler angles to turn : Step S303: Calculate the quaternion To the quaternion Euler angles that need to be turned And the rotation Euler vector : wherein denotes the scalar part of , , denote the first component, the second component, the third component of the vector part, respectively.

5. Quaternion to quaternion planned quaternion sequence length A planned quaternion sequence can be obtained as （ ）。 6. The geometric analysis based spacecraft attitude maneuver pointing constraint path planning method according to claim 1, wherein, The step S4 comprises: If the quaternion sequence of the spacecraft attitude maneuver path planning without the pointing constraint meets the pointing constraint, then the required path planning quaternion sequence is obtained; otherwise, the combined quaternion sequence is constructed as follows , The required path planning quaternion sequence is obtained. , The required path planning quaternion sequence is obtained. wherein , , , .

7. A geometric analysis based spacecraft attitude maneuver pointing constraint path planning system, characterized by, The method comprises the following steps: Module M1: calculating a quaternion sequence of a spacecraft attitude maneuver path planning without a pointing constraint; Module M2: judging whether the quaternion sequence of the spacecraft attitude maneuver path planning without the pointing constraint satisfies a spacecraft pointing constraint; if yes, the whole attitude planning is completed, otherwise, entering module M3; Module M3: calculating a quaternion sequence of a spacecraft attitude maneuver path planning between two critical attitude quaternions with the pointing constraint; Module M4: combining the quaternion sequences of the above steps to obtain a quaternion sequence of the spacecraft attitude maneuver path planning with the pointing constraint.

8. The geometric analysis based spacecraft attitude maneuver pointing constraint path planning system of claim 6, wherein, The module M1 comprises the following sub-modules: Module M101: calculating a quaternion from a current attitude of the spacecraft to a target attitude; wherein denotes the spacecraft target attitude quaternion, denotes the spacecraft current time attitude; Module M102: Calculates the spacecraft's attitude quaternion at the current moment. Quaternion of spacecraft target attitude Euler angles that need to be rotated and rotational Euler vector : wherein denotes the scalar part of , , denote the first component, the second component, the third component of the vector part, respectively. Module M103: Determine the number of quaternion sequences according to the plan and Calculate the spacecraft attitude maneuver path planning quaternion sequence without pointing constraints: （ ） Based on ( ), calculate and : where the pose transformation matrix is derived from the quaternion conversion.

9. The geometric analysis based spacecraft attitude maneuver pointing constraint path planning system of claim 6, wherein, In the module M2, the spacecraft attitude maneuver pointing constraint is judged as: The module M3 comprises the following sub-modules: wherein, denotes a vector in the spacecraft body coordinate system, denotes a vector in the J2000 inertial system, denotes the attitude transformation matrix from the spacecraft J2000 inertial system to the body system, if for all , all have then the spacecraft attitude maneuver path planning quaternion sequence under the non-directional constraint all satisfy the spacecraft directional constraint, at this time the entire attitude planning is completed, otherwise enter module M3.

10. The geometric analysis based spacecraft attitude maneuver pointing constraint path planning system of claim 6, wherein, The module M4 comprises: Module M301: according to the order from small to large, record in sequence the satisfying and store in array , record the length of array , , two critical quaternions satisfying the pointing constraint respectively;​ Module M302: Compute quaternions that satisfy the pointing constraints to quaternions between the planned quaternion sequence: Record use Will Project the vector into the system , with Will Project the vector into the system , by , The normal unit vector of the plane composed of , The normal unit vector of the plane composed of Computing quaternions To quaternions Euler angles to turn : Computing quaternions To quaternions Direction sign of rotation Euler vector Direction sign of rotation Euler vector : if , then , else ; wherein is a quaternion is converted into a pose transformation matrix to obtain is a quaternion is converted into a pose transformation matrix to obtain, denoted as ; According to the quaternion to the quaternion planned quaternion sequence length , a planned quaternion sequence is obtained （ ） Computing quaternions To quaternion Euler angles to turn : Module M303: Compute Quaternion To Quaternion Euler Angles to Turn And Rotation Euler Vector : According to the quaternion to the quaternion planned quaternion sequence length A planned quaternion sequence can be obtained （ ）。 11. The geometric analysis based spacecraft attitude maneuver pointing constraint path planning system according to claim 6, wherein, ​ If the quaternion sequence of the spacecraft attitude maneuver path planning without the pointing constraint meets the pointing constraint, then the required path planning quaternion sequence is obtained; otherwise, the combined quaternion sequence is constructed as follows , The required path planning quaternion sequence is obtained. , The required path planning quaternion sequence is obtained. wherein , , , .

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