CN114115319A - Spacecraft attitude maneuver path planning method under time-varying constraint - Google Patents
Spacecraft attitude maneuver path planning method under time-varying constraint Download PDFInfo
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Abstract
The invention relates to a spacecraft attitude maneuver path planning method under time-varying constraint, which is used for establishing a new attitude maneuver path planning model; sampling a rotating path of a characteristic shaft fixedly connected to a spacecraft in a celestial coordinate system at a fixed time interval delta t by utilizing an RRT-GoalBias method, judging whether the characteristic shaft meets time-varying constraint of direction until a group of path node sequences of which the characteristic shaft points to rotate from an initial direction to a target direction are obtained; the rotation between the two nodes is realized by one-time constant-speed fixed-axis rotation, and a state time curve of a quaternion of spacecraft attitude maneuver is obtained; the attitude maneuver spherical shell is used for describing the rotation time history of the characteristic axis and the change of a time-varying pointing constraint interval, reversely solving the time curve of the characteristic axis vector and the time envelope surface of a time-varying pointing constraint area from the obtained quaternion state time curve, drawing the time envelope surface in the attitude maneuver spherical shell, judging whether the characteristic axis meets the pointing constraint or not, and finishing the planning work of the spacecraft attitude maneuver path under the time-varying constraint.
Description
Technical Field
The invention relates to a spacecraft attitude maneuver path planning method under time-varying constraint, and belongs to the technical field of spacecraft control.
Background
Spacecraft attitude motion has an important role in many practical engineering tasks, including earth observation, observation of moving objects in space, and the like. In recent years, many new achievements are obtained in the research of path planning methods of spacecraft attitude motion under multiple constraints, and the constraints comprise two types[3]Pointing constraints from outside the spacecraft and control constraints from inside the spacecraft. Studies on internal dynamics and kinematic constraints have been achieved by controller design and are mature, while studies on external constraints have started to be late and are therefore a major issue in current studies. The external pointing constraints can be classified into a taboo constraint to avoid a specific pointing range and a forced constraint to maintain the specific pointing range according to the motion characteristics of the characteristic axes. Typical contra-constraints such as spacecraft attitude maneuver do not allow strong light celestial bodies (e.g., sun) to enter the field of view of the on-board optical sensor. Typical constraints include that the solar sailboard of the spacecraft be kept pointed to the sun, that the communication antenna be pointed to the earth, that the optical camera be pointed to the observation target, etc.
The multi-directional constrained attitude path planning method has achieved certain achievements at present. Frazzoli et al propose a method for planning an attitude path under multiple constraints based on a stochastic programming theory, but do not consider performance indexes of attitude maneuver. Cheng jun, etc[6]After the attitude planning problem is converted into a non-convex quadratic planning problem with optimal energy, a pseudo-spectrum method is used for solving, and a prediction control method is used for path node tracking, so that the pointing constraint of the nodes is met, but the algorithm efficiency is obviously reduced under the condition that the number of the nodes is increased. Wu et al propose a time coding strategy, and solve the time-optimal and energy-optimal attitude path planning problem based on a standard differential evolution algorithm and an improved differential evolution algorithm respectively under the condition of simultaneously considering taboo constraint and mandatory constraint. Celani et al propose a method based onSpacecraft attitude shortest time motion planning by derivative-free method of sequence penalty function[9]Meanwhile, the taboo area is avoided in the motion process, and the local optimal solution is avoided by adopting two target functions to carry out alternate search. Wang et al propose a constrained path diagram for fast planning of spacecraft attitude paths under multi-tabu constraint, and improve the search efficiency of the algorithm by using Euler forward search and node security search. Spiller et al combine inverse dynamics method and particle swarm optimization, and design time-optimal attitude maneuver path planning method satisfying tabu constraint [12 ]]But only for the case where the single axis pointing is constrained.
Although the existing spacecraft attitude path planning method considers the situation that multiple axes on a spacecraft simultaneously meet multiple pointing constraints, the pointing constraints are all time-invariant. When time-varying attitude pointing constraint exists, the path constraint condition suffered by spacecraft attitude maneuver is more complex, and the existing attitude maneuver path planning algorithm is difficult to apply. Meanwhile, in the existing research, the description of the attitude maneuver path with the pointing constraint depends on the maneuver path and the Mercator projection diagram of the maneuver path of the unit vector point in the constrained axis direction on the spacecraft on the unit spherical surface of the space coordinate system, and only can represent a time-invariant pointing constraint area, and the change of the pointing constraint under the time-varying constraint cannot be described.
Disclosure of Invention
The invention solves the problems: the method overcomes the defects of the prior art, provides a spacecraft attitude maneuver path planning method under time-varying constraint, and solves the problem of attitude maneuver path planning with time-varying pointing constraint. Meanwhile, the attitude maneuver spherical shell model is provided for reflecting the time attribute of the attitude maneuver path, and is convenient for checking whether the generated attitude maneuver path meets the time-varying path constraint.
The technical scheme of the invention is as follows: a spacecraft attitude maneuver path planning method under time-varying constraint is characterized by comprising the following steps:
step 1: expanding the time-invariant pointing constraint in the spacecraft attitude maneuver process into a time-variant pointing constraint, and establishing an attitude maneuver path planning model with the time-variant pointing constraint;
step 2: based on the attitude maneuver path planning model with time-varying direction constraint in the step 1, sampling the rotating direction of a characteristic shaft fixedly connected to the spacecraft by using an RRT-Goaldias method at a fixed time interval delta t in an celestial coordinate system to obtain the direction of the characteristic shaft at the next moment, judging whether the characteristic shaft meets the time-varying direction constraint, and obtaining a group of path node sequences of the characteristic shaft rotating from the initial direction to a target direction characteristic shaft through repeated sampling;
and step 3: the rotation between two nodes in the path node sequence of the characteristic shaft rotation obtained in the step 2 is realized by one-time constant-speed fixed-axis rotation, and a quaternion node sequence of the spacecraft attitude maneuver is reversely solved according to the characteristic shaft rotation path node sequence to obtain a quaternion state time curve of the spacecraft attitude maneuver;
and 4, step 4: and (3) providing an attitude maneuver spherical shell, which is used for describing a time course of the rotation of the characteristic axis and a time-varying pointing constraint area, reversely solving a time curve of the vector rotation path of the characteristic axis and an envelope surface of the time-varying pointing constraint area from the quaternion state time curve obtained in the step (3), and drawing the time curve and the envelope surface in the attitude maneuver spherical shell to visually judge whether the characteristic axis meets the time-varying pointing constraint or not, and finally finishing the planning work of the attitude maneuver path of the spacecraft under the time-varying constraint.
In step 1, the model is as follows:
in the problem of planning a spacecraft attitude maneuver path with orientation constraint, the constraint condition does not directly act on the attitude of the spacecraft, but limits the orientation of a certain device which is fixedly connected with the spacecraft, such as an optical camera, a solar panel and the like, and the orientation is defined as a characteristic axis. Therefore, the invention provides a method for planning the characteristic axis rotation path and then reversely deducing the attitude quaternion, which can more conveniently judge the satisfied condition of the pointing constraint in the attitude maneuver process. Meanwhile, the method can popularize the defined directional constraint from the time-invariant static constraint to the time-variant dynamic constraint without obviously increasing the difficulty of solving the path planning algorithm.
The orientation of the pose is usually constrained by constraintsThe axis of constraint and the angle of constraint, and therefore the directional constraint can be described as a constraint axis vector rC＝rC(t), restraint angle θC＝θC(t); describing directional tabu constraints as constraint axis vectors rF＝rF(t), restraint angle θF＝θF(t) of (d). Wherein both constraint axis vectors are unit vectors. Therefore, whether the pointing constraint is satisfied can be judged through the relation between the included angle between the characteristic axis and the constraint angle in the inertial system.
And combining the spacecraft attitude dynamics, the kinematics equation and the time-varying pointing constraint condition to obtain an attitude maneuver path planning model under the time-varying constraint.
In the step 1, an attitude maneuver path planning model with time-varying pointing constraints is established as follows:
(11) an objective function: max: rb_target(tf)·rT
rb_targetFor securing to a target characteristic axis on the spacecraft, tfAs the end time of the attitude maneuver, rTFor the target characteristic axis r in attitude maneuverb_targetFor determining the mission of a spacecraft attitude maneuver, max represents let rb_target(tf) Vector and target pointing rTThe dot product between the vectors is maximum, namely the included angle between the two vectors is minimum;
(12) and (3) dynamic constraint:
in the formula: the kinetic equation is given in the principal axis coordinate system of the spacecraft, J ═ diag (J)1,J2,J3) Is a spacecraft moment of inertia matrix, J1、J2And J3Is the main moment of inertia, u ═ u1,u2,u3]TRepresenting the attitude control moment of the spacecraft, omega ═ omega1,ω2,ω3]TRepresents an angular velocity;
(13) kinematic constraint:
in the formula:
is an attitude quaternion;
(14) boundary condition
The initial condition is an attitude quaternion q (t)0)＝Q0，t0The initial time of the attitude maneuver task is the terminal condition rb_target(tf)·rT>cos xi, xi is the rotation angle between two characteristic axis vector nodes, namely the rotation step length of each sampling;
(15) time varying orientation constraint
The time-invariant pointing constraints suffered by the spacecraft in the attitude maneuver process are classified into taboo constraints and forced constraints, wherein the taboo constraints refer to characteristic axes rbAnd given direction rFMust be greater than a given angle thetaF，rFCalled the tabu constraint axis, the constrained finger characteristic axis rbAnd given direction rCMust be less than a given angle thetaC，rCCalled a strongly constrained beam axis; the spacecraft is simultaneously provided with i characteristic axes { rb_n}b＝rn0N is 1,2, 1, i, and the target characteristic axis rb_target∈{rb_nAnd when the nth characteristic axis has nC forced constraint axes and the iF taboo constraint axes are, the taboo constraint and the forced constraint are respectively as follows:
contraindication and restriction: r isb_n(t)·rFn_mF(t)≤cosθFn_mF(t),n＝1,2,...,i；mF＝1,2,...,nF
And (3) forced constraint: r isb_n(t)·rCn_mC(t)≥cosθCn_mC(t),n＝1,2,...,i；mC＝1,2,...,nC
In the formula rb_nIs the nth characteristic axis vector, r, on the spacecraftFn_mFAnd rCn_mCRespectively for its mF-th forbidden axis and mC-th strong constrained axis, cos θFn_mFAnd cos θCn_mFRespectively corresponding to the constraint angles of the two constraint axes; for gestures under time-varying constraintsManeuvering path planning, constraining forcibly the axes and constraining angles as a function of time t, i.e. rC＝rC(t) and θC＝θC(t); similarly, the taboo constraint axis and the constraint angle also change with time rF＝rF(t) and θF＝θF(t)。
The step 2 is specifically realized as follows:
according to the attitude maneuver path planning model obtained in the step 1, the RRT-GoalBias method is used for sampling the characteristic axis path nodes, so that the characteristic axis is rotated from the initial direction to the target direction, and the method is specifically realized as follows:
(21) in a celestial coordinate system, the longitude angle and the latitude angle pointed by the characteristic axis are taken as state variables, and sampling is carried out in the azimuth space described by the longitude and the latitude by an RRT-Goalbias method to obtain a sampling pointing direction rsampThis step is referred to as "sampling";
(22) measuring the measurement between two directional nodes by using the included angle between vectors, and finding the R and the r from the current tree nodesampNode pointing axis r with minimum included anglenearestAs a new node rnewA parent node of (a);
(23) from the parent node to the sampling axis rsampAnd (3) carrying out fixed-axis rotation with the step length of the included angle xi once to obtain a sub node, wherein the rotating shaft is as follows:
(24) the time interval between the two nodes is set as a fixed value delta t, so the angular speed is xi/delta t;
(25) by defining sampling time, obtaining a pointing constraint axis and a constraint angle of a child node at the moment, judging whether the characteristic axis of the child node meets the pointing constraint, if so, adding the characteristic axis into the current spanning tree, and if not, abandoning the pointing constraint;
(26) and (4) iteratively carrying out sampling and expanding until a characteristic axis vector node sequence with the characteristic axis continuously rotating from the initial direction to the target direction is obtained.
The step 3 is specifically realized as follows:
according to the path of the characteristic axis rotating from the initial direction to the target direction obtained in the step 2, two nodes are rotationally connected by a constant-speed fixed axis within one time of delta t, and because the initial attitude is known and is expressed by a quaternion, the attitude quaternion at any moment in the rotating process can be calculated, and the method is specifically realized as follows:
(31) a rotation quaternion of xi about the R axis is given in the inertial system:
qr＝[cos(ξ/2),rxsin(ξ/2),rysin(ξ/2),rzsin(ξ/2)]T
(32) attitude quaternion of child node of
(33) The intermediate attitude between the two nodes is:
(34) and finally obtaining a quaternion time course of the attitude maneuver: q (t), t ∈ [0, t ]last]。
The step 4 is specifically realized as follows:
the conventional method draws a rotation path of a unit vector on a spherical surface in an celestial coordinate system, but cannot represent a time attribute and also cannot draw a time-varying constraint axis and a constraint angle. Therefore, the invention provides a posture maneuvering spherical shell, which expands a unit sphere by one unit along the radial direction to express the increment of time, and is realized by the following steps:
(41) using the attitude quaternion obtained in the step 3 to reversely solve a time curve r of the characteristic axis vectorb(t)：
(42) After obtaining the attitude maneuver path satisfying the time-varying constraint, accumulating the maneuver time Tmaneuver＝tlast-t0Time t corresponding to a path node for a reference valueLUnitization is carried out, namely:
(43) to be provided with
Drawing a time motion curve of the characteristic axis in the attitude maneuver sphere;
(44) and a time motion curve of a time-varying constraint axis vector in the attitude maneuver spherical shell is drawn in the same way, a time envelope tube of a constraint area can be obtained by combining a constraint angle time curve, the position relation between the characteristic axis time curve and the constraint envelope tube is observed, and whether the attitude maneuver path meets the time-varying pointing constraint or not can be visually judged.
Compared with the prior art, the invention has the advantages that:
(1) the requirement of an actual engineering task can be met only by strictly meeting pointing constraints in the spacecraft attitude maneuver process. The current attitude maneuver path planning algorithm only researches the time-invariant constraint aiming at the constrained model and does not analyze the time-variant constraint, so that a new attitude maneuver planning model needs to be established after the time-variant constraint is added, and the method is suitable for the planning problem of more attitude maneuver paths. On the basis of considering the time-invariant constraint attitude maneuver path planning method, the time-variant constraint condition is added, and the attitude maneuver path planning under the more complex constraint condition is realized. Meanwhile, the invention provides the attitude maneuver spherical shell, which expands the original spherical surface of the celestial body coordinate system along the radial direction and represents the time lapse by unitized radial outward expansion, so that the change of the pointing constraint can be described, and the attitude maneuver path can be conveniently and visually checked whether to effectively meet all path pointing constraint conditions;
(2) the existing time-invariant optimization is popularized to time-variant constraint, and the method is suitable for wider practical engineering problems;
(3) attitude maneuver meeting the pointing constraint is more easily realized by reversely deducing the attitude quaternion by utilizing the rotation path of the characteristic shaft;
(4) the time attribute is introduced into the traditional RRT-GoalBias method based on sampling, the path planning with time-varying constraint condition can be carried out, the limitation that the existing attitude maneuver path planning method only can consider the time-invariant orientation constraint can be broken through, and the application range of the attitude path planning method is expanded by introducing the time-varying orientation constraint;
(5) the time-varying constraint characteristic shaft rotation path display is carried out based on the proposed attitude maneuver spherical shell, so that the effectiveness of the attitude maneuver path can be conveniently and intuitively analyzed. In the existing method, the time-varying orientation constraint is not researched. The traditional RRT method has no time attribute when planning the path and can not avoid the dynamic constraint area. The traditional attitude maneuver path analysis can only be embodied by a time curve of each state quantity, and the integrated display of 'characteristic axis-constraint area-time' cannot be realized.
Drawings
FIG. 1 is a schematic diagram of spacecraft attitude pointing constraints;
FIG. 2 is a flow chart of the RRT-Goalbias algorithm;
FIG. 3 is a schematic diagram of a spacecraft multiaxis constraint;
FIG. 4 is an "expansion" block of the algorithm under the time-varying constraint of the present invention;
FIG. 5 is a schematic of a gesturing maneuver sphere shell constraint;
FIG. 6 is a time invariant constraint boundary diagram on a unit sphere;
FIG. 7 is a flow chart of a method for planning a maneuver path under time-varying constraints in accordance with the present invention;
FIG. 8 illustrates the characteristic axis maneuver paths in case one (1) of the present invention;
FIG. 9 shows the characteristic axis maneuvering path in case two (2) of the present invention;
FIG. 10 is the characteristic axis maneuver path in case two;
FIG. 11 is the attitude quaternion curve for case two.
Detailed Description
The present invention will be described in detail below with reference to the accompanying drawings and examples.
The attitude maneuver path planning of the spacecraft can adopt RRT and other sampling-based motion planning methods, and particularly avoids carrying out complex characteristic analysis on problems under the condition that various constraint conditions exist.
As shown in fig. 7, on the basis of performing attitude maneuver path planning based on the RRT method, the path nodes are matched with time, so that a time-varying directional constraint condition is introduced into a sampling and collision detection model, and attitude maneuver path planning including time-varying constraint is realized. Meanwhile, the invention unitizes the time corresponding to the maneuvering path node, and radially expands the unit spherical surface of the celestial body coordinate system into a spherical shell with the thickness of 1 unit, which is used for describing a time-varying pointing constraint area and a maneuvering path of the attitude containing time information in the maneuvering process of the attitude.
1. Spacecraft attitude motion model
The spacecraft attitude motion model comprises a kinetic equation and a kinematic equation. For rigid spacecraft, the kinetic equations can be derived by analysis of the theorem of angular momentum. In order to avoid singularity of the attitude description, the attitude is described by using quaternion, and a kinematic equation can be obtained.
In the formula: the kinetic equation is given in the principal axis coordinate system of the spacecraft, J ═ diag (J)1,J2,J3) Is a spacecraft moment of inertia matrix, J1、J2And J3Is the main moment of inertia, u ═ u1,u2,u3]TRepresenting the attitude control moment of the spacecraft, omega ═ omega1,ω2,ω3]TThe angular velocity is represented by the angular velocity,
is an attitude quaternion, q0And q isvScalar and vector parts which are quaternions respectively and satisfy | | q | | non-woven cells2＝1。
In practical engineering, the angular velocity and the control moment in each direction in the spacecraft system are often limited, namely, the absolute value of u is satisfiedi|≤umax,i,|ωi|≤ωmax,iAnd i is 1,2 and 3. The amplitude constraint of the state quantity can be realized through a proper controller design, and is not the key point of algorithm research in the invention, so that the attitude maneuver path planning algorithm provided by the invention emphasizes on whether a path node meets a constraint condition for analysis, and the attitude maneuver capability of the spacecraft can realize the path tracking, namely the upper bound of the amplitude of the control moment and the angular velocity component is considered to be large enough.
2. Time-varying constrained attitude maneuver path planning
2.1 planning of attitude maneuver path under time invariant constraint based on RRT-GoalBias method
The time-invariant pointing constraints suffered by the spacecraft in the attitude maneuver process are classified into taboo constraints and forced constraints, wherein the taboo constraints refer to characteristic axes rbAnd given direction rFMust be greater than a given angle thetaF，rFCalled the tabu constraint axis, the constrained finger characteristic axis rbAnd given direction rCMust be less than a given angle thetaC，rCReferred to as a strongly constrained beam axis, as shown in fig. 1. Taking the center of the spherical celestial body as the origin of an inertial space coordinate system and a target to be observed by the spacecraft; the five-pointed star celestial body is a distant strong light source celestial body, and an optical camera on the spacecraft needs to avoid a target. With rbIs a unit vector of the central direction of the view field of the optical camera on the spacecraft, theta is the view field included angle of theta, and rCUnit vector, r, for the spacecraft to point to the observation targetFThe unit vector of the spacecraft pointing to the strong light celestial body. Thus, in the inertial system, the taboo constraint and the mandatory constraint can be described by an equation and an equation, respectively, from the viewpoint of the characteristic axis.
rb·rF≤cosθ (3)
rb·rC≥cosθ (4)
Because components such as the optical camera are fixedly connected with the spacecraft body system, the calculation is restrictedWhen the conditions are met, the system O is calculated according to the current attitude quaternion qbTo the inertial system OICoordinate transformation matrix L ofIbThen, again by
Calculating r in the inertial systemb，rb,IAnd rb,bR in the inertial and body systems, respectivelybThe vector coordinates of (2). According to the relation between the attitude quaternion and the rotation matrix, the following can be obtained:
in the formula E3In the form of a third-order identity matrix,
is qvThe cross-product matrix of (a) is:
fast random search tree (RRT) is a sampling-based robot path planning method, has been applied to many cases in academic research and engineering application, and has also been used for spacecraft attitude maneuver path planning[14]. The RRT searches a path from a starting point to an end point by performing the steps of point sampling, collision judgment and node connection in a given space, and can avoid an obstacle area in the space. Because the efficiency of finding the movement towards the end point direction by completely random sampling is too low, the end point is usually directly taken as a sampling point with a certain probability during sampling, so that the efficiency of path search is improved, and the algorithm is RRT-GoalBias.
As shown in fig. 2, the RRT algorithm uses the starting point as a root node (initial spanning tree), continuously performs random sampling in a search space to obtain a sampling point, uses a node closest to the sampling point in the current spanning tree node as a parent node, and moves the parent node by a fixed step length in the direction of the sampling point to obtain a child node, and if the child node satisfies a constraint condition, adds the child node to the spanning tree, otherwise, performs resampling. The RRT-Goalbias algorithm directly takes the end point as a sampling point with the probability p0 during sampling, so that the efficiency of random sampling is improved.
And defining the direction of a component shaft fixedly connected to the spacecraft as a characteristic shaft of the spacecraft. In the problem of planning the attitude maneuver path with path constraint, the constraint area is specific to the characteristic axis rather than directly constraining the attitude of the spacecraft, so that the attitude maneuver path meeting the constraint condition can be searched more conveniently by reversely deducing the attitude of the spacecraft from the motion pointed by the characteristic axis during maneuvering.
In a celestial coordinate system, sampling is carried out by taking the longitude angle and the latitude angle pointed by the characteristic axis as state variables, and the measurement between nodes is measured by the included angle between two vectors. According to the Euler rotation theorem, two poses can be achieved by one rotation around space. Therefore, when the RRT-GoalBias method is used for attitude path planning, after the sampling direction is determined, the node vector with the minimum included angle with the sampling point vector can be found out from the existing nodes, and the preset included angle step xi is rotated towards the sampling point vector to obtain a new node. Let the sampling point pointing axis be rsampThe node axis nearest thereto is rnearestThen, there are:
if the new node satisfies the path constraint, it is connected to the existing spanning tree. Calculating the rotation quaternion q of the spacecraft by using the rotating shaft and the included angle of the characteristic shaft rotationr。
qr＝[cos(ξ/2),rxsin(ξ/2),rysin(ξ/2),rzsin(ξ/2)]T (8)
Quaternion q in the formularThe coordinate system is consistent with the rotating shaft R and is given in the inertial system. And then determining the attitude quaternion moving to the new node by the formula.
In the formula, qnewFor quaternion corresponding to the new node, qnearestAnd the quaternion corresponding to the node closest to the sampling point vector. If q is definedi(ti) Is tiAttitude quaternion of time, corresponding to last time tiThe attitude quaternion of (a) is qi-1(ti-1) Then satisfy
. The RRT-GoalBias method continues to generate new nodes through sampling and expanding operations until the end point is reached. The starting point and the end point of the path are described by vectors of characteristic axes, and it is noted that the attitude quaternion and the characteristic axis vector do not correspond to each other one by one, and the spacecraft attitude quaternion corresponding to the characteristic axis vector is not unique.
2.2 planning of attitude maneuver path under time-varying constraint based on RRT-GoalBias method
For the problem of planning attitude maneuver path under time-varying constraint, the beam axis r is strongly constrainedC＝rC(t) and the taboo restriction axis rF＝rF(t) must be determined before planning can begin. The change of the constraint angle can be considered when the constraint axis is changed, so that the cone angle of the forced constraint is thetaC＝θC(t) taper angle of tabu constraint is θF＝θF(t) of (d). When i characteristic axes are considered on the spacecraft, the nth characteristic axis has nC forced constraint axes, and nF tabu constraint axes, tabu constraint and forced constraint are respectively shown as formula:
rb_n(t)·rFn_mF(t)≤cosθFn_mF(t),n＝1,2,...,i；mF＝1,2,...,nF (10)
rb_n(t)·rCn_mC(t)≥cosθCn_mC(t),n＝1,2,...,i；mC＝1,2,...,nC (11)
in the formula rb_nIs the nth characteristic axis vector, r, on the spacecraftFn_mFAnd rCn_mCRespectively, its mF-th forbidden constraint axis and mC-th strong constraint axis. An example is given in fig. 3, a spacecraft has three characteristic axes,characteristic axis rb_1Having a time-invariant inhibiting axis rF1_1The constraint angle is constant at thetaF1_1(ii) a Characteristic axis rb_2With a time-invariant constraint axis rC2_1The constraint angle is constant at thetaC2_1(ii) a Characteristic axis rb_3Having a time-varying restraining axis rC3_1The constraint angle is constant at thetaC3_1. As can be seen from FIG. 3, rC3_1Moving from the initial solid line position to the dotted line position, and if the spacecraft does not perform attitude maneuver, then the characteristic axis rb_3The mandatory constraints on it will not be satisfied.
The conventional RRT-GoalBias method for sampling is only used for planning a path of a static map moving from a starting point to an end point, and a map with changed obstacle areas is inconvenient to directly use, because the RRT method only depends on distance information during sampling and does not consider time information. In order to apply the RRT-GoalBias method to pose path planning under time-varying constraint, the time property of its sampling point must be explained. In the invention, the time interval between the new node and the father node is a fixed time delta t, and the time interval has an included angle step size xi which is the same as that of 2.1 sections, so that the spacecraft attitude is realized by maneuvering from the father node to the new node through uniform rotation, and the rotation angular speed omegasampξ/Δ t, this causes an abrupt change in angular velocity at the intermediate node of the resulting attitude maneuver path. The abrupt change of the angular velocity can increase the difficulty of tracking the planned attitude maneuver path by the spacecraft through the control law design, so that the limitation is needed. The method is only used for solving the problem of planning the attitude maneuver path, and the attitude tracking problem can be solved according to the existing control algorithm.
The sequence number of the node in the path sequence obtained based on the RRT-GoalBias method is called the level L of the node, the level of the starting point is 1, therefore, the corresponding time of each node is tL(L-1) Δ t. By utilizing the time attribute of the node, the taboo constraint and the mandatory constraint under the time-varying constraint can be obtained as a formula and a formula respectively:
rb_n(tL)·rFn_mF(tL)≤cosθFn_mF(tL),n＝1,2,...,i；mF＝1,2,...,nF (12)
rb_n(tL)·rCn_mC(tL)≥cosθCn_mC(tL),n＝1,2,...,i；mC＝1,2,...,nC (13)
in the formula rb_n(tL) A new node of level L. After the change-in-time constraint is added, the "expansion" module in FIG. 2 needs to be modified, as shown in FIG. 4. When all the nodes on the obtained path meet the path constraint at each moment, the spacecraft can realize the attitude maneuver from the starting point to the end point and meet the time-varying attitude pointing constraint.
As shown in fig. 4, on the basis of the algorithm of fig. 2, since the level of the sampling node in the spanning tree determines the time attribute thereof, the "extension" module needs to be modified, and a one-step time-varying constraint condition calculation is added therein, so that the path constraint judgment of the new node can be performed.
Sampling and expanding are carried out iteratively until a sampling node is obtained and meets the iteration termination condition, namely rlast(tf)·rT>cos xi, where r islastIs the last sampling node; finally obtaining a group of characteristic axis vector node sequences { r0,r1,...,rlastFrom the sequence of the attitude maneuvering path nodes { r }0,r1,...,rlastSelecting and determining by r in the spanning treelastStarting, sequentially connecting father nodes forwards until a group of path node sequences { r ] are obtained after the father nodes are connected with the root node0,...,rlastAnd f, taking the target characteristic axis as a path for moving from the root node to the target node. Obtaining a corresponding node sequence { q ] of the attitude quaternion by using the same rotation mode as the rotation of the characteristic shaft0,...,qlastThe attitude maneuver between two nodes is realized by constant-speed fixed-axis rotation within a time of delta t, and q isi-1And q isiThere is a
t∈[ti-1,ti]Finally obtaining the quaternion time history q (t) of the attitude maneuver, wherein t belongs to [0, t ∈last]。
3. Attitude maneuver spherical shell
For spacecraft attitude maneuver path description under time-varying constraint, the spacecraft attitude maneuver path description cannot be described on a spherical surface in a traditional celestial coordinate system, so that the attitude maneuver spherical shell provided by the invention is used for spacecraft attitude maneuver path display under time-varying constraint. The attitude maneuver ball shell radially expands the unit ball by one unit to represent an incremental increase in time. After obtaining the attitude maneuver path satisfying the time-varying constraint, accumulating the maneuver time Tmaneuver＝tlast-t0Time t corresponding to a path node for a reference valueLUnitization is carried out, namely:
for a starting point, the rank is 1, then
For the last node of the path, there is tlast＝TmaneuverThen, then
With the gestured hull, the temporal attributes of the gestured path can be described along the unit radial direction. The attitude maneuver spherical shell can embody the time attribute of the characteristic axis rotation path, so the attitude maneuver under the invariant constraint for describing the time can also contain more information.
As shown in fig. 5, the inner sphere and the outer sphere of the attitude maneuver sphere define the characteristic axis vector boundaries at the initial time and the end time, respectively, and the middle tubular envelope surface is the boundary of the time-varying constraint region. And the constraint axis and the constraint angle at each moment are known, the pointing constraint at each moment in the attitude maneuver process is a circle on the spherical surface at the corresponding moment, and all constraint boundary circles are continuous in the radial direction due to the continuity of the constraint angles of the time-varying constraint axis, so that a tubular envelope in the spherical shell can be obtained.
As shown in fig. 6, the conventional time-invariant constraint may represent the constraint region boundary by one circle on the unit sphere determined by the fixed constraint axis and the constraint angle information.
The description of the characteristic axis vector is different from the point on the original unit spherical surface and is changed into the point in the attitude maneuver spherical shell, so that the characteristic axis needs to be subjected to vector extension according to the time attribute during description, and the requirement of meeting the requirement of vector extension on the characteristic axis
Is rbA corresponding vector in the gestural motor sphere. Therefore, the path of the characteristic axis changes from a curve on the unit spherical surface to a curve inside the attitude maneuver sphere shell, and satisfies that the start point and the end point fall on the inner spherical surface and the outer spherical surface, respectively.
The complete flow of the spacecraft attitude maneuver path planning method under the time-varying constraint is given in fig. 7. As shown in fig. 7, after an initial attitude quaternion and a characteristic axis vector in the system are given and a target direction of the characteristic axis vector in the inertial system is given, the method provided by the invention firstly calculates the initial direction of the characteristic axis vector in the inertial system, so that the attitude maneuver path planning problem is converted into a path planning problem of the characteristic axis vector in the inertial system, a characteristic axis vector rotation path under time-varying constraint is obtained by solving based on the RRT-GoalBias method, and then the attitude quaternion is further reversely pushed. And finally, representing the characteristic axis vector and the envelope surface of the time-varying constraint area in the attitude maneuver spherical shell, so that the effectiveness of the obtained attitude maneuver path is conveniently analyzed.
4. Simulation case
In order to verify the effectiveness of the attitude maneuver path planning algorithm under the time-varying constraint provided by the invention, two groups of simulation cases are provided, and attitude maneuver path planning under the tabu constraint and the forced constraint is respectively verified. Quaternion of initial attitude of spacecraft
The sampling angle step xi is 3 °, the sampling time interval Δ t is 10s, and the probability p0 that the target direction is pointed by the sampling point is 0.3.
Case one: attitude maneuver path planning under tabu constraint
(1) Forbidden axis in the inertial systemSwing at uniform speed around the z axis and restrict the cone angle thetaF15 deg. initial pointing
The oscillating angular velocity is:
in the formula: t isF200s is the period of oscillation. Characteristic axis target pointing at
(2) The restraint shaft is forbidden to rotate around the v axis at a constant speed while swinging around the z axis at a constant speed in an inertia system. The v-axis is defined as:
in the formula of UzIs a z-axis unit vector. The angular velocity ω about the v-axis is the same as in (1) with respect to the z-axisF,v＝0.12°/s。rF(tL+1) From rF(tL) First rotate around z-axis omegaF,zΔ t, rewind v (t)L) Rotation omegaF,vΔ t is obtained.
Case two: attitude maneuver path planning under forced constraint
The motion mode of the strong constraint beam axis is the same as that in case one (2), and the angular velocity of the beam swinging around the z axis is changed into:
period of oscillation TC120 s. Angular velocity omega of rotation about the v-axisC,v0.3 °/s. Characteristic axis target pointing is changed to
1. Case-attitude maneuver Path
As shown in fig. 8, the dashed arrow and the solid arrow respectively represent the initial direction and the target direction of the characteristic axis vector, and a curve in the spanning tree represents the motion path of the characteristic axis vector and does not enter the envelope of the pointing-prohibited region, so that it is known that the characteristic axis direction in the obtained attitude maneuver satisfies the time-varying constraint condition.
As shown in fig. 9, in the case that the change of the pointing-prohibited constraint area is more complicated, the present invention can still obtain the gesture maneuver path satisfying the constraint condition.
2. Case two-gesture maneuver Path
Under the condition of satisfying the mandatory constraint, the rotation of the characteristic axis from the initial point to the over-target point is more limited, and the gesture maneuver path can be finished only in the time period that the terminal point is contained in the mandatory constraint cone.
As shown in fig. 10, the characteristic axis vector is always kept in the envelope of the constrained region during the process of rotating from the initial pointing direction to the target pointing direction, and the time-varying constraint condition is satisfied, thus proving the effectiveness of the algorithm proposed by the present invention.
As shown in fig. 11, the time history of the attitude quaternion can be effectively obtained in the attitude maneuver process, and the modulo | q (t) | of the quaternion can be ensured to be 1, so that the characteristic axis vector at any moment can be reversely deduced. The algorithm in the invention can obtain the attitude maneuver path meeting the time-varying pointing constraint.
The above examples are provided only for the purpose of describing the present invention, and are not intended to limit the scope of the present invention. The scope of the invention is defined by the appended claims. Various equivalent substitutions and modifications can be made without departing from the spirit and principles of the invention, and are intended to be within the scope of the invention.
Claims (5)
1. A spacecraft attitude maneuver path planning method under time-varying constraint is characterized by comprising the following steps:
step 1: expanding the time-invariant pointing constraint in the spacecraft attitude maneuver process into a time-variant pointing constraint, and establishing an attitude maneuver path planning model with the time-variant pointing constraint;
step 2: based on the attitude maneuver path planning model with time-varying direction constraint in the step 1, sampling the rotating direction of a characteristic shaft fixedly connected to the spacecraft by using an RRT-Goaldias method at a fixed time interval delta t in an celestial coordinate system to obtain the direction of the characteristic shaft at the next moment, judging whether the characteristic shaft meets the time-varying direction constraint, and obtaining a group of path node sequences of the characteristic shaft rotating from the initial direction to a target direction characteristic shaft through repeated sampling;
and step 3: the rotation between two nodes in the path node sequence of the characteristic shaft rotation obtained in the step 2 is realized by one-time constant-speed fixed-axis rotation, and a quaternion node sequence of the spacecraft attitude maneuver is reversely solved according to the characteristic shaft rotation path node sequence to obtain a quaternion state time curve of the spacecraft attitude maneuver;
and 4, step 4: and (3) providing an attitude maneuver spherical shell, which is used for describing a time course of the rotation of the characteristic axis and a time-varying pointing constraint area, reversely solving a time curve of the vector rotation path of the characteristic axis and an envelope surface of the time-varying pointing constraint area from the quaternion state time curve obtained in the step (3), and drawing the time curve and the envelope surface in the attitude maneuver spherical shell to visually judge whether the characteristic axis meets the time-varying pointing constraint or not, and finally finishing the planning work of the attitude maneuver path of the spacecraft under the time-varying constraint.
2. The method for spacecraft attitude maneuver path planning under time-varying constraints of claim 1, characterized by: in the step 1, an attitude maneuver path planning model with time-varying pointing constraints is established as follows:
(11) an objective function: max: rb_target(tf)·rT
rb_targetFor securing to a target characteristic axis on the spacecraft, tfAs the end time of the attitude maneuver, rTFor the target characteristic axis r in attitude maneuverb_targetFor determining the mission of a spacecraft attitude maneuver, max represents let rb_target(tf) Vector and target pointing rTBetween vectorsThe point product is maximum, namely the included angle between the two vectors is minimum;
(12) and (3) dynamic constraint:
in the formula: the kinetic equation is given in the principal axis coordinate system of the spacecraft, J ═ diag (J)1,J2,J3) Is a spacecraft moment of inertia matrix, J1、J2And J3Is the main moment of inertia, u ═ u1,u2,u3]TRepresenting the attitude control moment of the spacecraft, omega ═ omega1,ω2,ω3]TRepresents an angular velocity;
(13) kinematic constraint:
in the formula:
is an attitude quaternion;
(14) boundary condition
The initial condition is an attitude quaternion q (t)0)＝Q0，t0The initial time of the attitude maneuver task is the terminal condition rb_target(tf)·rT>cos xi, xi is the rotation angle between two characteristic axis vector nodes, namely the rotation step length of each sampling;
(15) time varying orientation constraint
The time-invariant pointing constraints suffered by the spacecraft in the attitude maneuver process are classified into taboo constraints and forced constraints, wherein the taboo constraints refer to characteristic axes rbAnd given direction rFMust be greater than a given angle thetaF，rFCalled the tabu constraint axis, the constrained finger characteristic axis rbAnd given direction rCMust be less than a given angle thetaC，rCCalled a strongly constrained beam axis; the spacecraft is simultaneously provided with i characteristic axes { rb_n}b＝rn0N is 1,2, 1, i, and the target characteristic axis rb_target∈{rb_nAnd when the nth characteristic axis has nC forced constraint axes and the iF taboo constraint axes are, the taboo constraint and the forced constraint are respectively as follows:
contraindication and restriction: r isb_n(t)·rFn_mF(t)≤cosθFn_mF(t),n＝1,2,...,i；mF＝1,2,...,nF
And (3) forced constraint: r isb_n(t)·rCn_mC(t)≥cosθCn_mC(t),n＝1,2,...,i；mC＝1,2,...,nC
In the formula rb_nIs the nth characteristic axis vector, r, on the spacecraftFn_mFAnd rCn_mCRespectively for its mF-th forbidden axis and mC-th strong constrained axis, cos θFn_mFAnd cos θCn_mFRespectively corresponding to the constraint angles of the two constraint axes; for time-varying constrained attitude maneuver path planning, the constrained axes and constrained angles vary with time t, i.e., rC＝rC(t) and θC＝θC(t); similarly, the taboo constraint axis and the constraint angle also change with time rF＝rF(t) and θF＝θF(t)。
3. The method for spacecraft attitude maneuver path planning under time-varying constraints of claim 1, characterized by: the step 2 is specifically realized as follows:
(21) in a celestial coordinate system, the longitude angle and the latitude angle pointed by the characteristic axis are taken as state variables, and sampling is carried out in an azimuth space described by longitude and latitude by an RRT-Goalbias method to obtain the longitude psi and the latitude of a sampling azimuth
Then a sampling pointing vector is obtained as
This step is called sampling;
(22) measuring the measurement between two pointing nodes by using the included angle between vectors, and finding the sum r from all nodes of the current spanning treesampNode vector r with minimum included anglenearestR is tonearestAs a new node rnewA parent node of (a);
(23) from the parent node to the sampling axis rsampAnd (3) carrying out fixed-axis rotation with the step length of the included angle xi once to obtain a sub node, wherein the rotating shaft is as follows:
obtaining R through coordinate rotation transformation calculation according to the rotating shaft vector R and the rotating angle xinew；
(24) Setting the time interval between two nodes as a fixed value delta t, setting the angular velocity as xi/delta t, and generating a tree node sequence { r0，r1，...，rnEvery node vector riCorresponding time of tiFrom riOf parent node ri-1Corresponding time t ofi-1Is obtained with ti＝ti-1+ Δ t. Set a root node r0Corresponding time t0＝0；
(25) Obtaining a pointing constraint axis and a constraint angle of a child node at the moment by defining sampling time, judging whether the child node characteristic axis meets pointing constraint, and if so, determining rnewAdding the current spanning tree, called expansion, and if the orientation constraint is not satisfied, discarding rnew；
(26) And (3) carrying out sampling and expansion iteratively until a sampling node is obtained and meets an iteration termination condition, namely: r islast(tf)·rT> cos xi, where r islastIs the last sampling node; finally obtaining a group of characteristic axis vector node sequences { r0，r1，...，rlastFrom the sequence of the attitude maneuvering path nodes { r }0，r1，...，rlastSelecting and determining by r in the spanning treelastStarting, sequentially connecting father nodes forwards until a group of path node sequences { r ] are obtained after the father nodes are connected with the root node0，...，rlastAs target feature axis from root node to targetAnd marking the moving path of the node.
4. The method for spacecraft attitude maneuver path planning under time-varying constraints of claim 1, characterized by: the step 3 is specifically realized as follows:
(31) given in the inertial systemi-1Rotating xi to q about the R axisiRotational quaternion of (2):
qr＝[cos(ξ/2)，rxsin(ξ/2)，rysin(ξ/2)，rzsin(ξ/2)]T
(32) attitude quaternion of child node of
Calculating to obtain a characteristic axis path node sequence { r0，...，rlastThe corresponding attitude quaternion node sequence (q)0，...，qlast}；
(33) The attitude maneuver between two nodes is realized by constant-speed fixed-axis rotation within delta t, qi-1And q isiThe intermediate postures of the middle part are as follows:
(34) and finally obtaining a quaternion time course of the attitude maneuver:
q(t)，t∈[0，tlast]。
5. the method for spacecraft attitude maneuver path planning under time-varying constraints of claim 1, characterized by: in the step 4: a posture maneuvering spherical shell is used for radially expanding a unit sphere by one unit to represent the increment of time, and is realized as follows:
(41) using the attitude quaternion obtained in the step 3 to reversely solve a time curve r of the characteristic axis vectorb(t)：
(42) After obtaining the attitude maneuver path satisfying the time-varying constraint, accumulating the maneuver time Tmaneuver＝tlast-t0Time t corresponding to a path node for a reference valueLUnitization is carried out, namely:
(43) to be provided with
Drawing a time motion curve of the characteristic axis in the attitude maneuver sphere;
(44) and drawing a time motion curve of a time-varying constraint axis vector in the attitude maneuver spherical shell in the same manner, combining a constraint angle time curve to obtain an envelope surface of a constraint area, observing the position relation between a characteristic axis time curve and a constraint envelope pipe, and visually judging whether the attitude maneuver path meets the time-varying pointing constraint.
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