CN115158705B - Sectional polynomial spacecraft attitude maneuver track planning method - Google Patents
Sectional polynomial spacecraft attitude maneuver track planning method Download PDFInfo
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Abstract
The invention discloses a method for planning a maneuvering trajectory of a segmented polynomial spacecraft attitude, and belongs to the field of spacecraft attitude planning. The implementation method of the invention comprises the following steps: establishing a spacecraft large-angle attitude maneuver model and a pointing constraint attitude ball map; the initial pointing and the target pointing of the spacecraft sensor are determined, the gesture track of the spacecraft is represented by a polynomial, the pointing constraint, the dynamics constraint and the bounded constraint are sequentially met in a layered mode through a spherical three-dimensional path planning, inverse dynamics and heuristic binary time distribution method, the shortest gesture maneuvering time gesture track and the fixed gesture maneuvering time gesture track can be obtained, the gesture track planning efficiency is high, and the complex pointing constraint processing capability is high. The planned track is used as the input of the gesture controller, the nominal track is tracked in real time through the output moment of the controller, the gesture maneuver for avoiding the complex tabu area is realized, and the real-time performance and the adaptability of the tracking control can be improved. The invention is more suitable for on-board autonomous attitude planning.
Description
Technical Field
The invention relates to a method for planning a segmental polynomial spacecraft attitude maneuver trajectory, and belongs to the field of spacecraft attitude planning.
Background
Spacecraft attitude maneuver often faces multiple pointing constraints in complex spatial environments. Pointing constraints can be classified into forced constraints, which means that the spacecraft attitude must be kept near a certain orientation, and contra-constraints, which means that the spacecraft attitude cannot be near a certain orientation. The camera needs to be aligned with the shot object, the antenna needs to be aligned with the signal transmitter and the like belongs to forced constraint, and the camera needs to avoid strong light celestial bodies and the like from belonging to contraindication constraint. Furthermore, spacecraft attitude maneuver is subject to bounded constraints, dynamic constraints, etc., which result in limited space available for attitude maneuver.
Numerous scholars develop a rapid planning method for attitude maneuver, and the rapid planning method for attitude maneuver plans out a feasible solution for attitude maneuver in a short time, and can be roughly divided into a random planning method (Xu Rui,Wu Changqing,Zhu Shengying,et al.A rapid maneuver path planning method with complex sensor pointing constraints in the attitude space[J].Information Systems Frontiers,2017,19(4):945-953.)、, a geometric planning method (Xu Rui,Wang Hui,Xu Wenming,et al.Rotational-path decomposition based recursive planning for spacecraft attitude reorientation[J].ActaAstronautica,2018,143:212-220.)、, a space discretization method (Kjellberg,Lightsey.Discretized Quaternion Constrained Attitude Pathfinding[J].Journal ofGuidance,Control,and Dynamics,2016,39(3): 713-718.) and the like. The stochastic programming method has strong universality but lower programming efficiency in a high-dimensional space, and the programming solution has uncertainty; the geometrical planning method rapidly generates a gesture track in a deterministic manner, but is difficult to process complex pointing constraints; the spatial discretization method can handle complex pointing constraints, but requires the pre-creation of a spherical grid map.
In addition, the existing gesture planning feasible solution method only focuses on rapidly giving out feasible gesture tracks, ignores gesture maneuvering time, and has the problems that the gesture maneuvering time is overlong and the gesture maneuvering time cannot be determined.
Disclosure of Invention
Aiming at the problem of weaker processing capacity on complex pointing constraint in the existing gesture planning feasible solution searching method, the main purpose of the invention is to provide a segmentation polynomial spacecraft gesture maneuver trajectory planning method, which is used for rapidly planning gesture maneuver feasible solutions under complex pointing constraint, and obtaining a gesture maneuver nominal trajectory. According to the method, the gesture track of the spacecraft is represented by a polynomial, the directional constraint, the dynamic constraint and the bounded constraint are sequentially met in a layered mode through a spherical three-dimensional path planning, inverse dynamics and heuristic binary time distribution method, the shortest gesture maneuvering time gesture track and the fixed gesture maneuvering time gesture track can be obtained, the gesture track planning efficiency is high, the complex directional constraint processing capability is high, the complex tabu region can be avoided, and the adaptability of the method is improved.
The aim of the invention is achieved by the following technical scheme.
The invention discloses a method for planning a segmental polynomial spacecraft attitude maneuver trajectory, which comprises the steps of establishing a spacecraft large-angle attitude maneuver model and a directional constraint attitude ball map; determining initial pointing and target pointing of a spacecraft sensor, performing three-dimensional spherical path planning to obtain a three-dimensional pointing path node set, and converting the three-dimensional pointing nodes into gesture quaternion nodes; performing minimum acceleration track planning on the gesture quaternion nodes by adopting time average allocation and performing inverse dynamics processing to obtain an initial gesture track of the spacecraft; the bounded constraint is met through a heuristic binary time distribution optimization method, and the shortest gesture maneuvering time gesture track under complex constraint is obtained.
The invention discloses a method for planning a segmental polynomial spacecraft attitude maneuver trajectory, which comprises the following steps:
Step one, based on the gesture quaternion, establishing a dynamics equation and a kinematics equation of the rigid spacecraft, giving a bounded constraint and a pointing constraint, namely establishing a spacecraft large-angle gesture maneuver model, and giving a spacecraft gesture maneuver initial gesture and a target gesture.
Based on the attitude quaternion, a dynamic equation and a kinematic equation of the rigid spacecraft are established as follows:
Wherein: q= [ q 0,q1,q2,q3]T ] is a posture quaternion representing rotation from the body coordinate system to the inertial coordinate system, ω= [ ω 1,ω2,ω3]T ] represents the satellite angular velocity in the body coordinate system, j=diag (J 1,J2,J3) represents the inertia matrix of the satellite with respect to the body system, ω × is a cross-multiplied matrix form of ω, u= [ u 1,u2,u3]T is a control moment in the satellite body system, and
The moment bounded and angular velocity bounded constraints are expressed in the form:
ui≤umax i＝1,2,3 (4)
ωi≤ωmax i＝1,2,3 (5)
pointing constraints include tabu constraints and mandatory constraints, expressed in the form:
Wherein: r b is the direction vector of the laser principal axis under the inertial system, r s and r v are the principal axis of the tabu cone and the principal axis of the forced cone under the inertial system respectively, and θ s and θ v are the half angle of the tabu cone and the half angle of the forced cone under the inertial system respectively.
Step two, after a spacecraft large-angle attitude maneuver model is established, the initial pointing direction r 0 and the target pointing direction r f of the given spacecraft sensor are established. And (3) carrying out three-dimensional spherical path planning, wherein the path planning state space is a gesture sphere surface formed by unit vectors, and the new node is expanded in such a way that Euler rotation with the step length delta degrees is carried out from the current node to the random node, so that a three-dimensional pointing node is obtained, and the three-dimensional pointing node is converted into a gesture quaternion node.
In order to obtain the shortest attitude maneuver path by using fewer nodes, the capability of processing complex pointing constraints is improved, and as the optimization, the RRT (remote radio transmitter) -SMART algorithm is adopted for three-dimensional spherical path planning, so that complex tabu areas can be avoided, and the adaptability of the invention is improved.
And thirdly, expressing gesture quaternion components by using polynomials, adopting time average allocation, planning minimum acceleration track of gesture quaternion nodes, and performing inverse dynamics processing to obtain an initial gesture track of the spacecraft.
In order to save the calculation resources as much as possible on the premise of meeting the obstacle avoidance performance, the quaternion tracks of the quaternion nodes in adjacent postures are preferably represented by 5 th order polynomials.
The quaternion track of the quaternion nodes of adjacent gestures is represented by a 5 th order polynomial
Where q i (t), i=0, 1,2,3 are the 4 components of the pose quaternion.
Complex gesture trajectory is represented by a piecewise polynomial
The number of gesture quaternion nodes is n+1, the number of complex gesture tracks is n, q i, i=1, 2, …, n is a matrix formed by polynomial coefficients, and q i is obtained through minimum acceleration track planning closed-form solution, so that continuous and smooth complex gesture tracks are obtained.
The moment and angular velocity trajectories of the spacecraft according to equations (1) and (2) can be represented by the first and second derivatives of the quaternion, which are represented as follows
And (3) carrying out initial time distribution by adopting average time distribution, and carrying out inverse dynamics processing on the complex gesture tracks represented by the formula (10) represented by the formulas (1), (2), (11) and (12) to obtain initial gesture tracks of the spacecraft.
And step four, taking the initial gesture track obtained in the step three as heuristic information, carrying out deterministic optimization on the time distribution proportion, giving a gesture maneuvering time interval, and carrying out piecewise polynomial gesture track planning for a plurality of times by adopting a dichotomy, so that the angular speed or the control moment gradually approaches the corresponding maximum value until the shortest gesture maneuvering time gesture track is obtained.
The initial gesture track is used as heuristic information, wherein the heuristic information comprises a maximum angular speed omega m, an initial angular speed omega 0 and a terminal angular speed omega f, and the distance between adjacent nodes is the gesture quaternion included angle d s. The acceleration distance and the deceleration distance are calculated by
Wherein t 1 and t 2 are acceleration time and deceleration time, respectively, and d 1 and d 2 are acceleration distance and deceleration distance, respectively. If d 1+d2＜ds, then the neighbor node time interval t i is updated as follows
Where t m is the maximum acceleration time. If d 1+d2≥ds, then the neighbor node time interval t i is updated as follows
ti＝t1+t2 (15)
After the deterministic optimization is carried out on the time distribution proportion, a gesture maneuvering time interval [ T min,Tmax ] is given, and a dichotomy is adopted to carry out piecewise polynomial gesture track planning for many times, so that the angular speed or the control moment gradually approaches the corresponding maximum value until the shortest gesture maneuvering time gesture track is obtained.
The method also comprises the following steps: and (3) taking the track obtained in the step four as the input of a gesture controller, tracking the nominal track in real time through the output moment of the controller, realizing gesture maneuver for avoiding complex tabu areas, and improving the real-time performance and adaptability of tracking control.
The beneficial effects are that:
1. According to the method for planning the attitude maneuver track of the segmented polynomial spacecraft, disclosed by the invention, the attitude track of the spacecraft is represented by a polynomial, the directional constraint, the dynamic constraint and the bounded constraint are sequentially met in a layered manner through the spherical three-dimensional path planning, the inverse dynamics and the heuristic binary time distribution method, the shortest attitude maneuver time attitude track and the fixed attitude maneuver time attitude track can be obtained, the attitude track planning efficiency is high, the real-time performance of tracking control is improved, and the method is more suitable for on-board autonomous attitude planning.
2. According to the method for planning the attitude maneuver trajectories of the segmented polynomial spacecraft, disclosed by the invention, the spherical path planning is adopted to meet the pointing constraint, the inverse dynamics is adopted to meet the dynamics constraint, the heuristic binary time distribution method is adopted to meet the bounded constraint, the pointing constraint, the dynamics constraint and the bounded constraint are sequentially met in a layered manner, the complex pointing constraint processing capability is further high, the complex tabu region can be avoided, and the adaptability of the method is improved.
3. According to the method for planning the attitude maneuver trajectories of the segmented polynomial spacecraft, disclosed by the invention, the attitude quaternion components of the spacecraft are represented by polynomials, the attitude quaternion components are normalized, after the shortest attitude maneuver time attitude trajectories are obtained by solving, the attitude trajectories of any fixed attitude maneuver time (larger than the shortest attitude maneuver time) can be quickly solved, and the task with requirements on the attitude maneuver time is still applicable.
Drawings
FIG. 1 is a flow chart of a method for planning a motor trajectory of a segmented polynomial spacecraft disclosed by the invention.
Fig. 2 is a moment trace during spacecraft attitude maneuver.
Fig. 3 is an angular velocity trajectory during spacecraft attitude maneuver.
FIG. 4 is a quaternion trajectory during spacecraft attitude maneuver.
Fig. 5 is a three-dimensional pointing path of a sensor during spacecraft attitude maneuver.
Detailed Description
The invention will be further explained with reference to the drawings and examples
Example 1
As shown in fig. 1, the method for planning the attitude maneuver trajectory of the segmented polynomial spacecraft disclosed in the embodiment specifically comprises the following implementation steps:
Step one, a large-angle attitude maneuver model of the spacecraft is built by using the formulas (1) and (2), wherein the rotational inertia of the spacecraft body is diag (100,100,100) kg-m 2, moment limitation and angular velocity limitation are considered, the maximum moment u max = 1N-m, and the maximum angular velocity omega max = 0.1rad/s.
In order to embody the capability of the segmented polynomial spacecraft attitude maneuver trajectory planning method to process complex pointing constraints, 15 tabu cone constraints are considered, specific parameters are shown in table 1,
Table 1 points to constraint parameters
And step two, giving an initial direction r start＝[0.8867,-0.4603,0.0440]T, and a target direction r goal＝[-0.7922,-0.6099,0.0225]T to perform three-dimensional spherical path planning. The path planning algorithm selects RRT-SMART algorithm, step length is selected to be 1 degree when a new node is expanded, path planning state space is the attitude sphere surface formed by unit vectors, the planning result is shown in table 2, and total 7 attitude nodes divide an attitude maneuvering path into 6 sections.
Table 2 three-dimensional spherical path planning
And thirdly, expressing the gesture quaternion track of the adjacent node by using equations (7), (8) and (9) by using a 5-order polynomial, expressing the complex gesture track by using a segmentation polynomial by using equation (10), and expressing the moment track and the angular velocity track of the spacecraft by using equations (11) and (12) by using first-order and second-order derivatives of quaternions.
The initial time distribution adopts average time distribution, and inverse dynamics processing is carried out on the complex gesture track represented by the formula (10) by the formulas (1), (2), (11) and (12) to obtain an initial gesture track, and the coefficients of the initial gesture track are shown in the table 3
TABLE 3 initial polynomial attitude trajectory coefficients
And fourthly, taking the initial gesture track as heuristic information, carrying out deterministic optimization on the time distribution proportion, giving a gesture maneuvering time interval [10,100] s, and carrying out sectional polynomial gesture track planning for a plurality of times by adopting a dichotomy to obtain the gesture track of the shortest gesture maneuvering time. The gesture track consists of a moment track, an angular velocity track and a gesture quaternion track, which are respectively shown in the figure (2), the figure (3) and the figure (4). The pointing path of the sensor is shown in fig. 5, where the red area represents the contraindicated constraint area and the black curve represents the pointing path of the sensor. The polynomial posture track coefficient corresponding to the shortest posture maneuvering time is
TABLE 4 polynomial attitude trajectory coefficient for shortest attitude maneuver time
The foregoing detailed description has set forth the objects, aspects and advantages of the invention in further detail, it should be understood that the foregoing description is only illustrative of the invention and is not intended to limit the scope of the invention, but is to be accorded the full scope of the invention as defined by the appended claims.
Claims (2)
1. The method for planning the attitude maneuver trajectories of the segmented polynomial spacecraft is characterized by comprising the following steps of: comprises the following steps of the method,
Firstly, establishing a dynamic equation and a kinematic equation of a rigid spacecraft based on a gesture quaternion, and giving a bounded constraint and a pointing constraint, namely establishing a spacecraft large-angle gesture maneuver model and giving a spacecraft gesture maneuver initial gesture and a target gesture;
the first implementation method of the step is that,
Based on the attitude quaternion, a dynamic equation and a kinematic equation of the rigid spacecraft are established as follows:
Wherein: q= [ q 0,q1,q2,q3]T ] is a posture quaternion representing rotation from the body coordinate system to the inertial coordinate system, ω= [ ω 1,ω2,ω3]T ] represents the satellite angular velocity in the body coordinate system, j=diag (J 1,J2,J3) represents the inertia matrix of the satellite with respect to the body system, ω × is a cross-multiplied matrix form of ω, u= [ u 1,u2,u3]T is a control moment in the satellite body system, and
The moment bounded and angular velocity bounded constraints are expressed in the form:
ui≤umax i＝1,2,3 (4)
ωi≤ωmax i＝1,2,3 (5)
pointing constraints include tabu constraints and mandatory constraints, expressed in the form:
Wherein: r b is the direction vector of the laser main shaft under the inertial system, r s and r v are the tabu cone main shaft and the forced cone main shaft under the inertial system respectively, and theta s and theta v are the tabu cone half angle and the forced cone half angle under the inertial system respectively;
carrying out three-dimensional spherical path planning by adopting an RRT-SMART algorithm;
Step two, after a spacecraft large-angle attitude maneuver model is established, giving an initial pointing direction r 0 and a target pointing direction r f of a spacecraft sensor; carrying out three-dimensional spherical path planning, wherein the path planning state space is a gesture sphere surface formed by unit vectors, and the new node is expanded in such a way that Euler rotation with the step length delta degrees is carried out from the current node to the random node, so as to obtain a three-dimensional pointing node, and the three-dimensional pointing node is converted into a gesture quaternion node;
Step three, expressing gesture quaternion components by using polynomials, adopting time average allocation, planning minimum acceleration track of gesture quaternion nodes, and carrying out inverse dynamics processing to obtain an initial gesture track of the spacecraft;
Step four, taking the initial gesture track obtained in the step three as heuristic information, carrying out deterministic optimization on the time allocation proportion, giving a gesture maneuvering time interval, and carrying out piecewise polynomial gesture track planning for a plurality of times by adopting a dichotomy to enable the angular speed or the control moment to approach the corresponding maximum value gradually until the shortest gesture maneuvering time gesture track is obtained;
The realization method of the fourth step is that,
Taking the initial gesture track as heuristic information, wherein the heuristic information comprises a maximum angular speed omega m, an initial angular speed omega 0 and a terminal angular speed omega f, and the distance between adjacent nodes is a gesture quaternion included angle d s; the acceleration distance and the deceleration distance are calculated by
Wherein t 1 and t 2 are acceleration time and deceleration time, respectively, and d 1 and d 2 are acceleration distance and deceleration distance, respectively; if d 1+d2＜ds, then the neighbor node time interval t i is updated as follows
Wherein t m is the maximum acceleration time; if d 1+d2≥ds, then the neighbor node time interval t i is updated as follows
ti＝t1+t2 (15)
After the deterministic optimization is carried out on the time distribution proportion, a gesture maneuvering time interval [ T min,Tmax ] is given, and a dichotomy is adopted to carry out piecewise polynomial gesture track planning for many times, so that the angular speed or the control moment gradually approaches the corresponding maximum value until the shortest gesture maneuvering time gesture track is obtained;
the quaternion track of the quaternion nodes of adjacent gestures is represented by a 5 th order polynomial
Wherein q i (t), i=0, 1,2,3 are 4 components of the gesture quaternion;
Complex gesture trajectory is represented by a piecewise polynomial
Wherein, the number of gesture quaternion nodes is n+1, the complex gesture track is n sections, q i, i=1, 2, …, n is a matrix formed by polynomial coefficients, q i is obtained by closed solving of minimum acceleration track planning, and continuous and smooth complex gesture tracks are obtained;
the moment and angular velocity trajectories of the spacecraft according to equations (1) and (2) can be represented by the first and second derivatives of the quaternion, which are represented as follows
And (3) carrying out initial time distribution by adopting average time distribution, and carrying out inverse dynamics processing on the complex gesture tracks represented by the formula (10) represented by the formulas (1), (2), (11) and (12) to obtain initial gesture tracks of the spacecraft.
2. A segmented polynomial spacecraft attitude maneuver trajectory planning method as claimed in claim 1, wherein: and step five, taking the track obtained in the step four as the input of a gesture controller, tracking the nominal track in real time through the output moment of the controller, realizing gesture maneuver for avoiding complex tabu areas, and improving the real-time performance and adaptability of tracking control.
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