CN111310312A - Spacecraft obstacle avoidance track rapid planning method and device and computer equipment - Google Patents
Spacecraft obstacle avoidance track rapid planning method and device and computer equipment Download PDFInfo
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Abstract
The application relates to a method and a device for quickly planning obstacle avoidance tracks of a spacecraft and computer equipment. The method comprises the following steps: the method comprises the steps of obtaining a relative motion model between a service spacecraft and a target spacecraft, obtaining a nonlinear collision avoidance constraint model of an obstacle, determining the central position of a rotating time window according to the projection position of the obstacle on a connecting line of a track starting point and a track end point of the service spacecraft, determining the length of the rotating time window according to the maximum size of the obstacle and preset adjusting parameters, obtaining obstacle avoidance constraint according to the nonlinear collision avoidance constraint model and a rotating hyperplane of the obstacle in the rotating time window, and performing rapid planning of obstacle avoidance tracks of the spacecraft according to the obstacle avoidance constraint and the relative motion model. By adopting the method, the hyperplane constraint rotation can be matched with the motion of the spacecraft, and prior information is not needed.
Description
Technical Field
The application relates to the technical field of spacecraft trajectory planning, in particular to a method, a device and computer equipment for quickly planning obstacle avoidance trajectories of a spacecraft.
Background
The service spacecraft approaches the target spacecraft in a close range and performs on-orbit service operation on the target spacecraft, which is an important means for effectively prolonging the service life of the service spacecraft and improving the task performance of the service spacecraft. The increasing number of space fragments leads to a greater and greater risk of collision of the service spacecraft in the close proximity process, and obstacle avoidance trajectory planning is required.
The existing spacecraft obstacle avoidance trajectory planning method mainly comprises two types. One is an analytic-based method, the most common of which is the Artificial Potential Function (APF), and the basic idea is to construct a target gravitational field and an obstacle repulsive field in a state space to guide a spacecraft to realize collision avoidance in a maneuvering process. The method is firstly proposed by Khatib in the study of obstacle avoidance trajectory planning of a ground robot, McInnes introduces the method into the space field, and the method is widely applied to task scenes of autonomous rendezvous, on-orbit assembly, formation flight and the like of spacecrafts due to the advantages of high calculation efficiency, easiness in judgment of stability and the like. However, in a multi-obstacle scene, some points in the state space may have a total force of zero under the action of multiple fields, which may cause the spacecraft to fall into a local minimum point.
Another obstacle avoidance method is to introduce collision avoidance as a constraint condition into trajectory planning and solve the collision avoidance by an optimization theory. However, the nonlinear obstacle avoidance constraint can increase the calculation burden of the system, and the calculation result is sensitive to the initial value. In order to solve the problems, Park and the like firstly provide an in-plane rotating hyperplane method (Rotating hyperplane) under a model prediction control framework, replace the original nonlinear ellipsoid constraint by a group of rotating linear constraints, convert the nonlinear trajectory planning problem into a quadratic planning problem, and expand the nonlinear trajectory planning problem into a three-dimensional space by Weiss and the like. Subsequently, Park et al also propose a method of double hyperplane, namely, ellipsoid constraints are replaced by two linear hyperplane constraints tangent to the original obstacle ellipsoid, so as to further improve the solving efficiency, and a simulation knot is verified through numerical simulation and a floating platform test; zagaris expands it into three-dimensional space and compares its performance with the rotational hyperplane method and the direct linearization method.
Taking the example that two obstacles need to be avoided in the process of close-range approach of the service spacecraft, the actual feasible region of the maneuvering trajectory is the whole space except the two obstacles. If the existing rotating hyperplane method is adopted, the feasible region of each obstacle is a half space formed by a hyperplane perpendicular to a connecting line of the service spacecraft and the obstacle, and the intersection of the corresponding half spaces of the two obstacles is the feasible region of the existing rotating hyperplane method. However, the intersection of the two half spaces is far smaller than the actual feasible region, and even the case that the intersection is empty occurs, that is, the feasible region of the maneuver trajectory of the service spacecraft is zero, which results in failure of planning the obstacle avoidance trajectory. The essential cause of this problem is the mismatch of the rotation of the hyperplane and the motion of the serving spacecraft.
Disclosure of Invention
Therefore, in order to solve the technical problems, it is necessary to provide a method, a device and a computer device for rapidly planning obstacle avoidance trajectory of a spacecraft, which can solve the problem of mismatching between rotation of a hyperplane and motion of a service spacecraft.
A method for rapidly planning obstacle avoidance tracks of a spacecraft comprises the following steps:
obtaining a relative motion model between a service spacecraft and a target spacecraft;
acquiring a nonlinear collision avoidance constraint model of the barrier;
determining the central position of a rotating time window according to the projection position of the barrier on a connecting line of a track starting point and a track end point of the service spacecraft;
determining the length of the rotating time window according to the maximum size of the obstacle and preset adjusting parameters;
obtaining obstacle avoidance constraint according to the nonlinear collision avoidance constraint model and a rotating hyperplane of the obstacle in the time window;
and rapidly planning the obstacle avoidance track of the spacecraft according to the obstacle avoidance constraint and the relative motion model.
In one embodiment, the method further comprises the following steps: acquiring a discrete form relative motion kinetic equation obtained by dispersing a service spacecraft and a target spacecraft in a sampling period T; superposing and recombining the state vector and the control input vector in the kinetic equation to obtain a relative motion model as follows:
X＝Ψx(0)+ΩU
where X represents a state column vector, U represents a control input column vector, and Ψ and Ω represent state transition matrices.
In one embodiment, the method further comprises the following steps: constructing a spatial ellipsoid no-fly region according to a covariance matrix corresponding to the measurement information of the obstacle; and determining a nonlinear collision avoidance constraint model of the barrier according to the space ellipsoid flight forbidding area, the position vector of the service spacecraft and the position vector of the center of the barrier.
In one embodiment, the method further comprises the following steps: according to the projection position of the barrier on the connecting line of the track starting point and the track end point of the service spacecraft, the central position of the rotating time window is determined as follows:
wherein, twindowIndicates the center position, dcpRepresenting the distance of the projection position from the start of the trajectory, dctIndicating the distance, T, from the end of the track to the start of the trackentireRepresenting the time of service spacecraft trajectory maneuvers [. ]]Indicating a rounding down.
In one embodiment, the method further comprises the following steps: according to the maximum size of the obstacle and preset adjusting parameters, determining the length of the rotating time window as follows:
wherein L iswindowRepresents the length of the rotation time window, ζ represents an adjustment coefficient for adjusting the hyperplane constraint rotation rate,
representing the maximum size of the obstacle.
In one of the embodiments, the first and second electrodes are,further comprising: unit vector r from center of obstacle to start point of the track and end point of the tracksAnd rg；
According to the unit vector rsAnd rgTo obtain the total rotation angle gamma of the hyperplanetot＝arccos(rs·rg)；
Obtaining discrete step number N in the rotating time windowwindowAccording to said discrete step number NwindowObtaining the angle gamma of the hyperplane rotating in each sampling period T in the rotating time windowtot/Nwindow(ii) a Wherein the hyperplane is at the NthkAt a sampling time compared with rsAngle of rotation of gammakComprises the following steps:
wherein N isstartAnd NendRespectively representing the number of the initial steps and the number of the ending steps in the rotating time window;
obtaining unit vector r by using the Rodrigue rotation formulasRotating gammakThe angle is used to obtain the corresponding unit vector rkComprises the following steps:
rk＝rscos(γk)+(k×rs)sin(γk)+k(k·rs)(1-cos(γk))；
wherein k is (r)s×rg)/|rs×rg| represents a unit vector of the rotating shaft;
obtaining a unit vector r according to the nonlinear collision avoidance constraint modelkPoint of intersection p with the surface of the obstaclekAnd at the intersection point pkEllipsoid normal vector n ofkAccording to the point of intersection pkAnd vector nkObtaining obstacle avoidance constraint as follows:
wherein e iskRepresenting the center of the obstacle to the point of intersection pkVector of (2)，ρkRepresenting the center of the obstacle to the current position of the serving spacecraft.
In one embodiment, the method further comprises the following steps: acquiring an optimal planning target, and establishing a target function according to the optimal planning target; determining a constraint condition according to the obstacle avoidance constraint and the relative motion model; and solving the objective function according to the constraint condition to realize rapid planning of the obstacle avoidance track of the spacecraft.
A spacecraft obstacle avoidance trajectory fast planning device, the device comprising:
the motion model building module is used for obtaining a relative motion model between the service spacecraft and the target spacecraft;
the collision model building module is used for obtaining a nonlinear collision avoidance constraint model of the barrier;
the rotating time window setting module is used for determining the central position of a rotating time window according to the projection position of the barrier on the connecting line of the track starting point and the track end point of the service spacecraft; determining the length of the rotating time window according to the maximum size of the obstacle and preset adjusting parameters;
the track planning module is used for obtaining obstacle avoidance constraint according to the nonlinear collision avoidance constraint model and a rotating hyperplane of the obstacle in the rotating time window; and rapidly planning the obstacle avoidance track of the spacecraft according to the obstacle avoidance constraint and the relative motion model.
A computer device comprising a memory and a processor, the memory storing a computer program, the processor implementing the following steps when executing the computer program:
obtaining a relative motion model of a service spacecraft and a target spacecraft;
acquiring a nonlinear collision avoidance constraint model of the barrier;
determining the central position of a rotating time window according to the projection position of the barrier on a connecting line of a track starting point and a track end point of the service spacecraft;
determining the length of the rotating time window according to the maximum size of the obstacle and preset adjusting parameters;
obtaining obstacle avoidance constraints according to the nonlinear collision avoidance constraint model and a rotating hyperplane of the obstacle in the rotating time window;
and rapidly planning the obstacle avoidance track of the spacecraft according to the obstacle avoidance constraint and the relative motion model.
A computer-readable storage medium, on which a computer program is stored which, when executed by a processor, carries out the steps of:
obtaining a relative motion model of a service spacecraft and a target spacecraft;
acquiring a nonlinear collision avoidance constraint model of the barrier;
determining the central position of a rotating time window according to the projection position of the barrier on a connecting line of a track starting point and a track end point of the service spacecraft;
determining the length of the rotating time window according to the maximum size of the obstacle and preset adjusting parameters;
obtaining obstacle avoidance constraints according to the nonlinear collision avoidance constraint model and a rotating hyperplane of the obstacle in the rotating time window;
and rapidly planning the obstacle avoidance track of the spacecraft according to the obstacle avoidance constraint and the relative motion model.
According to the rapid planning method, the rapid planning device, the rapid planning computer equipment and the rapid planning storage medium for the obstacle avoidance trajectory of the spacecraft, the hyperplane constraint is only rotated on the rotation time window through constructing the rotation time window, and the method is applied to a multi-obstacle scene, so that the defect that the constraint mutual interference in the multi-obstacle scene in the traditional method is effectively overcome, in addition, the center position of the rotation window is determined by utilizing the projection of the center of the obstacle on the connecting line of the starting position and the ending position of the service spacecraft, the hyperplane constraint rotation is matched with the motion of the service spacecraft, and no prior information is needed.
Drawings
Fig. 1 is a schematic flow chart of a method for rapidly planning an obstacle avoidance trajectory of a spacecraft in one embodiment;
FIG. 2 is a diagram of an ellipsoid structure in one embodiment;
FIG. 3 is a schematic diagram of a rotating window arrangement in one embodiment;
FIG. 4 is a schematic diagram of a rotated hyperplane within a rotated time window in one embodiment;
FIG. 5 is a schematic view of the collision avoidance trajectory of embodiment 1;
FIG. 6 is a schematic diagram of the collision avoidance trajectory of embodiment 2;
FIG. 7 is a schematic view of a collision avoidance trajectory according to another embodiment of example 1;
FIG. 8 is a schematic view of a collision avoidance trajectory according to example 2 of another embodiment;
fig. 9 is a block diagram of a fast planning apparatus for obstacle avoidance trajectory of a spacecraft in an embodiment;
FIG. 10 is a diagram showing an internal structure of a computer device according to an embodiment.
Detailed Description
In order to make the objects, technical solutions and advantages of the present application more apparent, the present application is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the present application and are not intended to limit the present application.
In one embodiment, as shown in fig. 1, a method for rapidly planning an obstacle avoidance trajectory of a spacecraft is provided, and the method may be applied to a terminal, and includes the following steps:
and 102, acquiring a relative motion model between the service spacecraft and the target spacecraft.
Under the relative motion coordinate system, the relative motion of the service spacecraft and the target spacecraft in the space is researched, and a basis is made for the trajectory planning of the subsequent service spacecraft.
And 104, acquiring a nonlinear collision avoidance constraint model of the obstacle.
The obstacle has potential threat to the flight of the service spacecraft, so that the range where the obstacle is located must be avoided during trajectory planning, and therefore, a nonlinear collision avoidance constraint model can be constructed based on the shape and the position of the obstacle.
And step 106, determining the central position of the rotating time window according to the projection position of the obstacle on the connecting line of the track starting point and the track ending point of the service spacecraft.
When planning the track, the starting point and the end point of the track need to be determined, in this step, the concept of rotating the time window is introduced, and the center position of the rotating time window is determined by using the idea of projection.
And step 108, determining the length of the rotating time window according to the maximum size of the obstacle and preset adjusting parameters.
By determining the length of the rotating time window, the setting of the rotating time window parameters is completed.
And 110, obtaining obstacle avoidance constraint according to the nonlinear collision avoidance constraint model and the rotating hyperplane of the obstacle in the rotating time window.
When rotating the hyperplane, operation is only performed in the rotating time window.
And 112, rapidly planning the obstacle avoidance track of the spacecraft according to the obstacle avoidance constraint and the relative motion model.
In the rapid planning method for the obstacle avoidance trajectory of the spacecraft, the rotating time window is constructed, the hyperplane constraint is only rotated on the rotating time window, and the method is applied to a multi-obstacle scene, so that the defect that the constraint mutual interference of the traditional method in the multi-obstacle scene is effectively overcome, in addition, the central position of the rotating window is determined by utilizing the projection of the center of the obstacle on the connecting line of the starting position and the tail position of the service spacecraft, the hyperplane constraint rotation is matched with the motion of the service spacecraft, and no prior information is needed.
In one embodiment, a discrete form relative motion kinetic equation obtained by dispersing a serving spacecraft and a target spacecraft in a sampling period T is obtained; superposing and recombining the state vector and the control input vector in the kinetic equation to obtain a relative motion model as follows:
X＝Ψx(0)+ΩU
where X represents a state column vector, U represents a control input column vector, and Ψ and Ω represent state transition matrices.
Specifically, X actually represents a column vector formed by superimposing relative states X (k) at all discrete times, where k is 1,2, …, N. x (k) is a 6 × 1 column vector.
Specifically, under the relative motion coordinate system, the service spacecraft relative motion equation can be expressed as:
wherein the content of the first and second substances,
denotes the state of relative motion, a ═ axayaz]TShowing the thrust accelerations in three directions and,
representing the average orbital angular velocity of the serving spacecraft.
Further, given a sampling period T, the discrete form of the kinetic equation can be obtained as:
wherein k is the current step number,
can be expressed as:
corresponding to impulse thrust model
Comprises the following steps:
to facilitate numerical solution, we step NThe state vector is superposed as X ═ X (1)T,x(2)T,…,x(N)T]T∈R6N×1The control input vector may also be recombined as U ═ U (0)T,u(1)T,…,u(N-1)T]T∈R3N×1Thus, a relative motion model can be obtained as:
X＝Ψx(0)+ΩU
where X represents a state column vector, U represents a control input column vector, Ψ and Ω represent state transition matrices, and where,
in one embodiment, a space ellipsoid no-fly region is constructed according to a covariance matrix corresponding to measurement information of the obstacle, and a nonlinear collision avoidance constraint model of the obstacle is determined according to the space ellipsoid no-fly region, a position vector of a service spacecraft and a position vector of a center of the obstacle.
Specifically, for the problem of obstacle avoidance of the service spacecraft, a three-dimensional ellipsoidal space no-fly zone containing the position where the obstacle may appear is usually introduced as the collision avoidance constraint. If the serving spacecraft trajectory intersects the obstacle ellipsoid, then the collision avoidance constraint is considered violated. The ellipsoid structure is shown in fig. 2, and the uncertainty of the ground observation device on its state estimation is large due to the small size of the obstacle, so the volume of the ellipsoid may be much larger than the actual size of the obstacle. After the ellipsoid structure is constructed, the obstacle is replaced by the ellipsoid structure, so that when the parameters of the obstacle are utilized, the parameters corresponding to the ellipsoid structure need to be acquired for parameter calculation. In some embodiments, if an ellipsoid structure is used to replace the obstacle or the obstacle is used for description, it can be known that the parameter corresponding to the ellipsoid is obtained.
In conjunction with the ellipsoid equation, the nonlinear collision avoidance constraint model can be expressed as:
(rpos-re)TS(rpos-re)≥1
wherein r isposA position vector, r, representing the serving spacecraft relative to the origin of the reference coordinate systemeAnd S is a shape matrix of an ellipsoid.
In practical applications, the uncertainty of the state estimation is usually quantized to gaussian noise and corresponding covariance matrix, and the main reason for selecting the ellipsoidal no-fly region is that the covariance matrix can be directly used to define an uncertainty ellipsoid, whose size is related to the probability of the real obstacle being located in the ellipsoid. n isσThe shape matrix S of the ellipsoid may be formed of nσThe inverse of the square of (d) and the covariance matrix sigma product:
the obstacle is located at nσThe probability within an ellipsoid can be expressed as:
for three-dimensional problems, it can be calculated from the above formula when nσWhen 3, the probability of an obstacle lying within an ellipsoid is 97.07%, when nσWhen 4, the probability is 99.74%.
In one embodiment, according to the projection position of the obstacle on the connecting line between the track starting point and the track ending point of the service spacecraft, the center position of the rotation time window is determined as follows:
wherein, twindowIndicates the center position, dcpIndicating the distance from the center position to the start of the track, dctIndicating the distance, T, from the end of the track to the start of the trackentireRepresenting the time of service spacecraft trajectory maneuvers [. ]]Indicating a rounding down. It should be noted that the center position of the time window, i.e., the center time, is rotated, and therefore, the center position is expressed in terms of time.
Specifically, the nonlinear collision avoidance constraint model requires a long calculation time in the solving process, and the result is sensitive to the initial value. The rotating hyperplane method constructs a series of rotating hyperplanes on the boundary of a two-dimensional obstacle ellipsoid and converts the non-linear ellipsoid no-fly zone constraint into a group of linear constraints, thereby ensuring that the service spacecraft is positioned outside the obstacle ellipsoid in each step. The linear constraint obtained by the rotating hyperplane method can not only improve the solving efficiency, but also ensure the feasibility of the obtained solution due to the convexity of the constraint.
As shown in fig. 3, a schematic diagram of a rotating window is provided, the center position of the rotating time window is determined by the projection of the center of the obstacle on the line of the starting and ending positions of the serving spacecraft, and the length can be determined by a tuning parameter ζ. In the figure, the projection of No. 1 obstacle center on the connection line of the starting position and the ending position of a service spacecraft is shown as r0And rfStraight distance d betweenctCan be expressed as:
dct＝|x0-xf|
wherein | is the modular length of the vector, the distance d from the projection point 1 to the initial position of the service spacecraftcp1Comprises the following steps:
then design No. 1 rotating window is centered on:
wherein [. ]]To round down the symbol, TentireFor task time, dcp1And dctRespectively representing the distances of the projection point 1 and the target position to the initial point.
In another embodiment, the length of the rotating time window is determined according to the maximum size of the obstacle and preset adjustment parameters as follows:
wherein L iswindowRepresents the length of the rotation time window, ζ represents an adjustment coefficient for adjusting the hyperplane constraint rotation rate,
representing the maximum size of the obstacle.
Specifically, in fig. 3, the maximum size of the obstacle No. 1 is
The time length of the rotation window # 1 is set as:
where ζ is the coefficient used to adjust the hyperplane-constrained rotation rate.
In one embodiment, the unit vector r is based on the center of the obstacle to the start of the trajectory and the end of the trajectorysAnd rg(ii) a According to unit vector rsAnd rgTo obtain the total rotation angle gamma of the hyperplanetot＝arccos(rs·rg) (ii) a Obtaining discrete step number N in rotating time windowwindowAccording to discrete step number NwindowObtaining the angle gamma of the hyperplane rotating in each sampling period T in the rotating time windowtot/Nwindow(ii) a Wherein the hyperplane is at the NthkAt a sampling time compared with rsIs gammakComprises the following steps:
wherein N isstartAnd NendRespectively representing the number of the initial steps and the number of the ending steps in the rotating time window; obtaining unit vector r by using the Rodrigue rotation formulasRotating gammakThe angle is used to obtain the corresponding unit vector rkComprises the following steps:
rk＝rscos(γk)+(k×rs)sin(γk)+k(k·rs)(1-cos(γk))；
wherein k is (r)s×rg)/|rs×rg| represents a unit vector of the rotating shaft; obtaining a unit vector r according to a nonlinear collision avoidance constraint modelkPoint of intersection p with the surface of the obstaclekAnd at the intersection point pkEllipsoid normal vector n ofkAccording to the point of intersection pkAnd vector nkObtaining obstacle avoidance constraint as follows:
wherein e iskRepresenting the center of the obstacle to the point of intersection pkVector of (a), pkA vector representing the center of the obstacle to the current position of the serving spacecraft.
Specifically, in fig. 3, the start time and the end time of the rotation window No. 1 are respectively:
the corresponding discrete steps are respectively as follows:
therefore, only in Nstart1Rotating the hyperplane after step to reach Nend1When the rotation is stopped, the hyperplane is stopped.
The hyperplane constraint rotation method in the rotating window is consistent with the traditional method, and hyperplane constraints outside the rotating window are initial hyperplane constraints and end hyperplane constraints respectively and are kept unchanged. By introducing the concept of rotating time windows, the problems of mutual interference between different obstacle constraints and mismatch between the hyperplane rotation and the motion of the serving spacecraft can be effectively alleviated. In addition, the overlap between different rotation windows can be adjusted by the adjustment parameter ζ in the formula.
As shown in fig. 4, providingFirstly, a unit vector r from the center of an obstacle to the starting and ending positions of a service spacecraft can be determined according to the position information of the obstacle and the service spacecraftsAnd rgThe angle between the two vectors will be taken as the total rotation angle gamma of the hyperplanetotWherein γ istot＝arccos(rs·rg)。
Secondly, according to the discrete step number N in the rotating time windowwindowDivide the total rotation angle gamma equallytotThe angle γ of each step in the rotating window can be obtainedtot/NwindowThen the hyperplane is at the NthkStep ratio rsIs gammak：
R is expressed by the Rodrigue rotation formulasRotating gammakThe angle is used to obtain the corresponding unit vector rk：
rk＝rscos(γk)+(k×rs)sin(γk)+k(k·rs)(1-cos(γk))
Wherein k is (r)s×rg)/|rs×rgAnd | is a unit vector of the rotating shaft. Then combining an ellipsoid equation to solve to obtain a unit vector rkPoint of intersection p with the surface of the obstaclekAnd the normal vector n of the ellipsoid at the pointk(ii) a Finally, center the obstacle to pkAnd the vector of the current serving spacecraft position is denoted e respectivelykAnd ρkThe obstacle avoidance constraint can be reconstructed as follows:
intersection point p and normal vector before and after rotating windownRespectively using NstartAnd NendAnd (3) step-corresponding intersection points and normal vectors, and then the obstacle avoidance constraint can be further expressed in a matrix form:
-ΗΩU≤-Ηε+ΗΨx0
wherein h and e are defined as:
in one embodiment, when the track planning is carried out, an optimal planning target is obtained, and a target function is established according to the optimal planning target; determining a constraint condition according to the obstacle avoidance constraint and the relative motion model; and solving an objective function according to the constraint conditions to realize rapid planning of the obstacle avoidance track of the spacecraft.
Specifically, the energy most province is selected as an optimal planning target, and the expression is as follows:
the constraint is then determined as:
x(t0)＝x0x(tf)＝xf
-umax≤ui≤umax(i＝x,y,z)
through observation, the performance index of the obstacle avoidance track planning problem is in a quadratic form, the constraint is linear constraint, and the existing quadratic planning method can be used for quickly solving the problem so as to realize the quick planning of the obstacle avoidance track. The invention adopts a quadprog solver in an MATLAB optimization toolbox to carry out secondary planning, and the specific form is as follows: solving the control sequence U such that:
simultaneously, the following requirements are met:
inequality in planning obstacle avoidance trajectory of spacecraft is taken as constraint and mainly comprises collision avoidance constraint and control input saturation constraint, and then matrix AineqAnd bineqCan be further expressed as:
equality constraint matrix AeqAnd beqCan be expressed as:
the energy savings as an objective function can be expressed as a quadratic form, then Π and f are:
the advantageous effects of the present invention will be described below with specific test data.
Assuming that the target spacecraft is located on a near-circular orbit with an orbit height of 500km, the initial and terminal relative states of the service spacecraft are respectively set as:
x0＝[0m 5000m 0m 0m/s 0m/s 0m/s]T
xf＝[0m 10m 0m 0m/s 0m/s 0m/s]T
the maximum pulse thrust of the service spacecraft is 10N, the mass is 100kg, and the time length of the whole task is 1000 s; numerical simulation is realized based on MATLAB 2016b, and the simulation computer is configured as follows: intel Core i7 processor, 8GRAM, 2.93GHz dominant frequency.
In the simulation, the performance of the window rotating hyperplane method in a multi-obstacle scene is evaluated by arranging two obstacle ellipsoids between the initial position and the target position of the service spacecraft. For convenience of description, the two obstacles are named a and B, respectively, and their covariance matrices are set as:
ΞA＝ΞB＝diag([3×104,3×104,1×105])m2
the center of the obstacle A is fixed at [500,700,0 ]]Tm, the center of the barrier B is respectively arranged at [ -100,4000,0 ] in different calculation examples]Tm and [ -100,3500,0]Tm to simulate a scene with two obstacles far away (example 1) and near (example 2). Because the center of the obstacle and the start and end positions of the service spacecraft are both positioned in the oxy plane, in order to simplify the operation, the relative motion track in the oxy plane is only considered in the embodiment.
In addition, in order to further verify the performance of the window rotation hyperplane method, a nonlinear ellipse method and a traditional rotation hyperplane method are adopted for comparison verification under the same problem configuration. The trajectory planning problem based on the nonlinear ellipse method can be converted into a nonlinear programming problem, the fmincon function of an MATLAB optimization toolbox is adopted to carry out numerical solution, and the precision parameters 'TolX', 'TolFun' and 'TolCon' of a solver are all set to be 1.0 multiplied by 10-6. Since the initial value of the nonlinear programming problem has a large influence on the calculation efficiency, the control input when the obstacle constraint is not considered is used as the initial guess value in the embodiment. The linear quadratic programming problem based on the hyperplane method adopts a quadprog function as a solver. And taking energy consumption and time required by calculation as evaluation indexes of track performance, wherein the energy consumed by the track is as follows:
the hyperplane of each obstacle can rotate clockwise and counterclockwise, so it is assumed that the hyperplane of obstacle a constrains clockwise rotation and B constrains counterclockwise rotation. The collision-prevention trajectory generated by the three methods described above in the embodiment 1 is shown in fig. 5, and the collision-prevention trajectory generated by the embodiment 2 is shown in fig. 6, where "NEM", "IRHM" and "CRHM" respectively represent the nonlinear ellipse method, the improved window rotation hyperplane method, and the conventional rotation hyperplane method, and the ratio of performance indexes of the three methods is shown in table 1.
TABLE 1 Performance index comparison (defining rotational direction)
Fig. 5 shows that when two obstacles are far apart, the three methods can successfully generate collision avoidance tracks, wherein the track generated by the window rotating hyperplane method is generally consistent with the track generated by the nonlinear ellipse method, and the track of the conventional rotating hyperplane method has a large difference from the other two methods. As can be seen from table 1, the energy consumption of the conventional rotational hyperplane method for generating the trajectory is much more than that of the other two methods. When two obstacles are close to each other, due to mutual interference between hyperplane constraints of the two obstacles, a feasible collision avoidance track cannot be generated by the conventional rotating hyperplane method, so that only the tracks of the nonlinear ellipse method and the window rotating hyperplane method are shown in fig. 6, and the two obstacles are still very close to each other. Compared with the nonlinear method, the window rotation hyperplane method provided by the invention has higher solving efficiency compared with the nonlinear method.
Further, the non-linear ellipse method is used to repeatedly solve the calculation example 2 for 500 times, wherein only 271 times can successfully generate a feasible track, and the average calculation time is much longer than that of a linearization method represented by a rotating hyperplane technology, so that the calculation efficiency of the non-linear ellipse method on the multi-obstacle collision avoidance problem is considered to be low, and convergence is not easy.
And when the rotating direction of the hyperplane corresponding to each obstacle is not limited, traversing the hyperplane to restrain all possible rotating direction combinations, and selecting a task track with the optimal performance from the task track. Simulations were also conducted in the above-described simulation configuration, and the collision avoidance trajectories and performance indexes thereof obtained in comparative example 1 and comparative example 2 are shown in fig. 7, fig. 8, and table 2, respectively. When the two obstacles are far away, the task track generated by the traditional rotating hyperplane method still consumes more energy than the other two methods, but the energy consumption is obviously improved compared with the situation that the rotating direction is limited by the hyperplane. Different from fig. 6, the conventional rotating hyperplane method can also generate a feasible collision avoidance trajectory when two obstacles are relatively close to each other, which further illustrates that all possible rotation direction combinations need to be considered comprehensively when the rotating hyperplane method is used to generate the collision avoidance trajectory. It is noted that, since it is necessary to calculate a plurality of rotation direction combinations, the calculation time of the rotation hyperplane method in table 2 is more than that of the corresponding index in table 1.
TABLE 2 comparison of Performance indicators (without limiting rotation direction)
The simulation result shows that the window rotation hyperplane method has better performance by comprehensively considering the energy consumption and the calculation timeliness of different collision avoidance methods.
It should be understood that, although the steps in the flowchart of fig. 1 are shown in order as indicated by the arrows, the steps are not necessarily performed in order as indicated by the arrows. The steps are not performed in the exact order shown and described, and may be performed in other orders, unless explicitly stated otherwise. Moreover, at least a portion of the steps in fig. 1 may include multiple sub-steps or multiple stages that are not necessarily performed at the same time, but may be performed at different times, and the order of performance of the sub-steps or stages is not necessarily sequential, but may be performed in turn or alternately with other steps or at least a portion of the sub-steps or stages of other steps.
In one embodiment, as shown in fig. 9, there is provided a fast planning apparatus for obstacle avoidance trajectory of spacecraft, including: a motion model construction module 902, a collision model construction module 904, a rotation time window setting module 906, and a trajectory planning module 908, wherein:
a motion model construction module 902, configured to obtain a relative motion model between the serving spacecraft and the target spacecraft;
a collision model construction module 904 for obtaining a nonlinear collision avoidance constraint model of the obstacle;
a rotating time window setting module 906, configured to determine a center position of a rotating time window according to a projection position of the obstacle on a connection line between a track start point and a track end point of the serving spacecraft; determining the length of the rotating time window according to the maximum size of the obstacle and preset adjusting parameters;
a trajectory planning module 908, configured to obtain an obstacle avoidance constraint according to the nonlinear collision avoidance constraint model and a rotating hyperplane of the obstacle within the rotating time window; and rapidly planning the obstacle avoidance track of the spacecraft according to the obstacle avoidance constraint and the relative motion model.
In one embodiment, the motion model building module 902 is further configured to obtain a discrete form relative motion kinetic equation obtained by discretizing the serving spacecraft and the target spacecraft by a sampling period T; superposing and recombining the state vector and the control input vector in the kinetic equation to obtain a relative motion model as follows:
X＝Ψx(0)+ΩU
where X represents a state column vector, U represents a control input column vector, and Ψ and Ω represent state transition matrices.
In one embodiment, the collision model building module 904 is further configured to build a spatial ellipsoid no-fly region according to a covariance matrix corresponding to the measurement information of the obstacle; and determining a nonlinear collision avoidance constraint model of the barrier according to the space ellipsoid flight forbidding area, the position vector of the service spacecraft and the position vector of the center of the barrier.
In one embodiment, the rotating time window setting module 906 is further configured to determine, according to the projection position of the obstacle on the connecting line between the starting point of the trajectory and the ending point of the trajectory of the service spacecraft, the central position of the rotating time window as:
wherein, twindowIndicates the center position, dcpRepresenting the distance of the projection position from the start of the trajectory, dctIndicating the distance, T, from the end of the track to the start of the trackentireRepresenting the time of service spacecraft trajectory maneuvers [. ]]Indicating a rounding down.
In one embodiment, the rotating time window setting module 906 is further configured to determine the length of the rotating time window as follows according to the maximum size of the obstacle and a preset adjustment parameter:
wherein L iswindowRepresents the length of the rotation time window, ζ represents an adjustment coefficient for adjusting the hyperplane constraint rotation rate,
representing the maximum size of the obstacle.
In one embodiment, the trajectory planning module 908 is further configured to calculate a unit vector r from the center of the obstacle to the start point and the end point of the trajectorysAnd rg；
According to the unit vector rsAnd rgTo obtain the total rotation angle gamma of the hyperplanetot＝arccos(rs·rg)；
Obtaining discrete step number N in the rotating time windowwindowAccording to said discrete step number NwindowObtaining the angle gamma of the hyperplane rotating in each sampling period T in the rotating time windowtot/Nwindow(ii) a Wherein the hyperplane is at the NthkAt a sampling time compared with rsIs gammakComprises the following steps:
wherein N isstartAnd NendRespectively representing the number of the initial steps and the number of the ending steps in the rotating time window;
obtaining unit vector r by using the Rodrigue rotation formulasRotating gammakThe angle is used to obtain the corresponding unit vector rkComprises the following steps:
rk＝rscos(γk)+(k×rs)sin(γk)+k(k·rs)(1-cos(γk))；
wherein k is (r)s×rg)/|rs×rg| represents a unit vector of the rotating shaft;
obtaining a unit vector r according to the nonlinear collision avoidance constraint modelkPoint of intersection p with the surface of the obstaclekAnd at the intersection point pkEllipsoid normal vector n ofkAccording to the point of intersection pkAnd vector nkObtaining obstacle avoidance constraint as follows:
wherein e iskRepresenting the center of the obstacle to the point of intersection pkVector of (a), pkA vector representing the center of the obstacle to the current position of the serving spacecraft.
In one embodiment, the trajectory planning module 908 is further configured to obtain an optimal planning target, and establish an objective function according to the optimal planning target; determining a constraint condition according to the obstacle avoidance constraint and the relative motion model; and solving the objective function according to the constraint condition to realize rapid planning of the obstacle avoidance track of the spacecraft.
For specific limitations of the device for rapidly planning the obstacle avoidance trajectory of the spacecraft, reference may be made to the above limitations of the method for rapidly planning the obstacle avoidance trajectory of the spacecraft, and details are not described here. All modules in the rapid planning device for the obstacle avoidance trajectory of the spacecraft can be completely or partially realized through software, hardware and a combination of the software and the hardware. The modules can be embedded in a hardware form or independent from a processor in the computer device, and can also be stored in a memory in the computer device in a software form, so that the processor can call and execute operations corresponding to the modules.
In one embodiment, a computer device is provided, which may be a terminal, and its internal structure diagram may be as shown in fig. 10. The computer device includes a processor, a memory, a network interface, a display screen, and an input device connected by a system bus. Wherein the processor of the computer device is configured to provide computing and control capabilities. The memory of the computer device comprises a nonvolatile storage medium and an internal memory. The non-volatile storage medium stores an operating system and a computer program. The internal memory provides an environment for the operation of an operating system and computer programs in the non-volatile storage medium. The network interface of the computer device is used for communicating with an external terminal through a network connection. The computer program is executed by a processor to realize a rapid planning method for the obstacle avoidance trajectory of the spacecraft. The display screen of the computer equipment can be a liquid crystal display screen or an electronic ink display screen, and the input device of the computer equipment can be a touch layer covered on the display screen, a key, a track ball or a touch pad arranged on the shell of the computer equipment, an external keyboard, a touch pad or a mouse and the like.
Those skilled in the art will appreciate that the architecture shown in fig. 10 is merely a block diagram of some of the structures associated with the disclosed aspects and is not intended to limit the computing devices to which the disclosed aspects apply, as particular computing devices may include more or less components than those shown, or may combine certain components, or have a different arrangement of components.
In an embodiment, a computer device is provided, comprising a memory storing a computer program and a processor implementing the steps of the method in the above embodiments when the processor executes the computer program.
In an embodiment, a computer-readable storage medium is provided, on which a computer program is stored, which computer program, when being executed by a processor, carries out the steps of the method in the above-mentioned embodiments.
It will be understood by those skilled in the art that all or part of the processes of the methods of the embodiments described above can be implemented by hardware instructions of a computer program, which can be stored in a non-volatile computer-readable storage medium, and when executed, can include the processes of the embodiments of the methods described above. Any reference to memory, storage, database, or other medium used in the embodiments provided herein may include non-volatile and/or volatile memory, among others. Non-volatile memory can include read-only memory (ROM), Programmable ROM (PROM), Electrically Programmable ROM (EPROM), Electrically Erasable Programmable ROM (EEPROM), or flash memory. Volatile memory can include Random Access Memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in a variety of forms such as Static RAM (SRAM), Dynamic RAM (DRAM), Synchronous DRAM (SDRAM), Double Data Rate SDRAM (DDRSDRAM), Enhanced SDRAM (ESDRAM), Synchronous Link DRAM (SLDRAM), Rambus Direct RAM (RDRAM), direct bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM).
The technical features of the above embodiments can be arbitrarily combined, and for the sake of brevity, all possible combinations of the technical features in the above embodiments are not described, but should be considered as the scope of the present specification as long as there is no contradiction between the combinations of the technical features.
The above-mentioned embodiments only express several embodiments of the present application, and the description thereof is more specific and detailed, but not construed as limiting the scope of the invention. It should be noted that, for a person skilled in the art, several variations and modifications can be made without departing from the concept of the present application, which falls within the scope of protection of the present application. Therefore, the protection scope of the present patent shall be subject to the appended claims.
Claims (10)
1. A method for rapidly planning obstacle avoidance tracks of a spacecraft comprises the following steps:
obtaining a relative motion model between a service spacecraft and a target spacecraft;
acquiring a nonlinear collision avoidance constraint model of the barrier;
determining the central position of a rotating time window according to the projection position of the barrier on a connecting line of a track starting point and a track end point of the service spacecraft;
determining the length of the rotating time window according to the maximum size of the obstacle and preset adjusting parameters;
obtaining obstacle avoidance constraints according to the nonlinear collision avoidance constraint model and a rotating hyperplane of the obstacle in the rotating time window;
and rapidly planning the obstacle avoidance track of the service spacecraft according to the obstacle avoidance constraint and the relative motion model.
2. The method of claim 1, wherein obtaining the model of relative motion between the serving spacecraft and the target spacecraft comprises:
acquiring a discrete form relative motion kinetic equation obtained by dispersing a service spacecraft and a target spacecraft in a sampling period T;
superposing and recombining the state vector and the control input vector in the kinetic equation to obtain a relative motion model as follows:
X＝Ψx(0)+ΩU
where X represents a state column vector, U represents a control input column vector, and Ψ and Ω represent state transition matrices.
3. The method of claim 1, wherein the obtaining a non-linear collision avoidance constraint model of the obstacle comprises:
constructing a spatial ellipsoid no-fly region according to a covariance matrix corresponding to the measurement information of the obstacle;
and determining a nonlinear collision avoidance constraint model of the barrier according to the space ellipsoid flight forbidding area, the position vector of the service spacecraft and the position vector of the center of the barrier.
4. The method of claim 1, wherein determining the center position of the rotating time window based on the projected position of the obstacle on the connecting line of the starting point and the ending point of the trajectory of the service spacecraft comprises:
according to the projection position of the barrier on the connecting line of the track starting point and the track end point of the service spacecraft, the central position of the rotating time window is determined as follows:
wherein, twindowIndicates the center position, dcpRepresenting the distance of the projection position from the start of the trajectory, dctIndicating the distance, T, from the end of the track to the start of the trackentireRepresenting the time of service spacecraft trajectory maneuvers [. ]]Indicating a rounding down.
5. The method of claim 4, wherein determining the length of the rotating time window based on the maximum size of the obstacle and a preset adjustment parameter comprises:
according to the maximum size of the obstacle and preset adjusting parameters, determining the length of the rotating time window as follows:
wherein L iswindowRepresents the length of the rotation time window, ζ represents an adjustment coefficient for adjusting the hyperplane constraint rotation rate,
representing the maximum size of the obstacle.
6. The method according to any one of claims 1 to 5, wherein obtaining obstacle avoidance constraints according to the nonlinear collision avoidance constraint model and a rotating hyperplane of an obstacle within the rotating time window comprises:
unit vector r from center of obstacle to start point of the track and end point of the tracksAnd rg；
According to the unit vector rsAnd rgTo obtain the total rotation angle gamma of the hyperplanetot＝arccos(rs·rg)；
Obtaining discrete step number N in the rotating time windowwindowAccording to said discrete step number NwindowObtaining the angle gamma of the hyperplane rotating in each sampling period T in the rotating time windowtot/Nwindow(ii) a Wherein the hyperplane is at the NthkAt a sampling time compared with rsIs gammakComprises the following steps:
wherein N isstartAnd NendRespectively representing the number of the initial steps and the number of the ending steps in the rotating time window;
obtaining unit vector r by using the Rodrigue rotation formulasRotating gammakThe angle is used to obtain the corresponding unit vector rkComprises the following steps:
rk＝rscos(γk)+(k×rs)sin(γk)+k(k·rs)(1-cos(γk))；
wherein k is (r)s×rg)/|rs×rg| represents a unit vector of the rotating shaft;
obtaining a unit vector r according to the nonlinear collision avoidance constraint modelkPoint of intersection p with the surface of the obstaclekAnd at the intersection point pkEllipsoid normal vector n ofkAccording to the point of intersection pkAnd vector nkObtaining obstacle avoidance constraint as follows:
wherein e iskRepresenting the center of the obstacle to the point of intersection pkVector of (a), pkA vector representing the center of the obstacle to the current position of the serving spacecraft.
7. The method according to claim 6, wherein performing fast planning of spacecraft obstacle avoidance trajectory according to the obstacle avoidance constraints and the relative motion model comprises:
acquiring an optimal planning target, and establishing a target function according to the optimal planning target;
determining a constraint condition according to the obstacle avoidance constraint and the relative motion model;
and solving the objective function according to the constraint condition to realize rapid planning of the obstacle avoidance track of the spacecraft.
8. A spacecraft obstacle avoidance track rapid planning device is characterized in that the device comprises:
the motion model building module is used for obtaining a relative motion model between the service spacecraft and the target spacecraft;
the collision model building module is used for obtaining a nonlinear collision avoidance constraint model of the barrier;
the rotating time window setting module is used for determining the central position of a rotating time window according to the projection position of the barrier on the connecting line of the track starting point and the track end point of the service spacecraft; determining the length of the rotating time window according to the maximum size of the obstacle and preset adjusting parameters;
the trajectory planning module is used for obtaining obstacle avoidance constraints according to the nonlinear collision avoidance constraint model and the rotating hyperplane where the obstacles are located; and rapidly planning the obstacle avoidance track of the spacecraft according to the obstacle avoidance constraint and the relative motion model.
9. A computer device comprising a memory and a processor, the memory storing a computer program, wherein the processor implements the steps of the method of any one of claims 1 to 7 when executing the computer program.
10. A computer-readable storage medium, on which a computer program is stored, which, when being executed by a processor, carries out the steps of the method of any one of claims 1 to 7.
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