CN113722821A - Method for making spacecraft rendezvous and docking trajectory planning event constraint convex - Google Patents

Method for making spacecraft rendezvous and docking trajectory planning event constraint convex Download PDF

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CN113722821A
CN113722821A CN202110991804.2A CN202110991804A CN113722821A CN 113722821 A CN113722821 A CN 113722821A CN 202110991804 A CN202110991804 A CN 202110991804A CN 113722821 A CN113722821 A CN 113722821A
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尚海滨
赵梓辰
袁怡婷
喻志桐
徐瑞
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Beijing Institute of Technology BIT
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Abstract

The invention discloses a method for making a spacecraft rendezvous and docking trajectory planning event constraint convex, and belongs to the technical field of aerospace. The implementation method of the invention comprises the following steps: discretizing the event constraint solution space to obtain a series of spatially discrete grids; calculating a constraint function value at each discrete grid boundary point, and interpolating constraint function data to obtain a linear expression form of the constraint function; constructing an event detection function, relaxing the event constraint function, and judging constraint by a convex grid to obtain a convex event constraint function form; constructing a switch function, describing an original event trigger function, and obtaining a convex expression form of the event trigger function; and solving the convex expression form to obtain an optimal trajectory for rendezvous and docking of the spacecraft, so that the convergence and efficiency of planning the rendezvous and docking trajectory of the spacecraft with the event constraint are improved on the premise of not changing the original problem solution space.

Description

Method for making spacecraft rendezvous and docking trajectory planning event constraint convex
Technical Field
The invention relates to a method for constraining and protruding a spacecraft trajectory planning event, which is particularly suitable for constraining and protruding the spacecraft rendezvous and docking trajectory planning event and belongs to the technical field of aerospace.
Background
The spacecraft trajectory planning is a key technology for realizing deep space exploration and near-earth space tasks, and has important application value in spacecraft rendezvous and docking tasks. Due to the fact that docking events exist in the spacecraft rendezvous and docking tasks, rendezvous and docking tracks of the spacecraft are discontinuous, and discontinuous event constraints exist when the rendezvous and docking tracks are planned. On one hand, how to overcome discontinuity, process event constraints and obtain a constraint form convenient for trajectory planning is a difficult point to be solved. On the other hand, the trajectory planning problem of spacecraft rendezvous and docking is essentially an optimal control problem, and for constraints in the optimal control problem, the constraint has a convex property, so that the problem planning efficiency can be effectively improved, the problem solving difficulty is reduced, and how to realize the convexity of event constraints is also a key problem to be solved. The processing method of the event constraint is one of the hot problems concerned by the current science and technology personnel.
In the developed event constraint processing method, in the prior art [1] (Jewison C m. "Guidance and control for multi-stage rendering and locking operations in the presence of non-certainty," Massachusetts Institute of Technology,2017), a convex method based on zero-one variable is proposed for discontinuous event constraint, and event triggering and non-triggering are described using zero-one variable and coupled in the kinetic equation. The method has the advantages of simple operation and no introduction of excessive optimization variables. However, in this method, introducing a zero-one variable causes a problem of trajectory planning NP to be difficult, and although a convex constraint form is obtained, the problem of trajectory planning problem is further caused to be poor in convergence and low in convergence efficiency, and it is difficult to apply to a problem of rendezvous and docking of spacecraft, which has a high requirement on robustness.
In prior art [2] (Lu, P. "Convex-Concave composition of Nonlinear Equipment Constraints in Optimal controls," Journal of guidelines, controls, and Dynamics,2020), we propose a bump Decomposition method, treating event Constraints as a zero-valued programming problem and sequence approximation of the zero-valued variables using non-integer optimized variables. The method can effectively solve the problem of NP difficulty caused by zero-variable introduction, but can cause the sequence iteration characteristic of the trajectory planning method, reduce the calculation efficiency and be difficult to be applied to the problem of rendezvous and docking of the spacecraft, which has higher requirement on the calculation rapidity.
Disclosure of Invention
In order to solve the problems of low computational efficiency and poor convergence frequently occurring when the existing method carries out trajectory planning event constraint projection, the invention discloses a projection method for trajectory planning event constraint butting in rendezvous of spacecraft, which aims to solve the technical problems that: on the premise of not adopting a sequence approximation method, the event constraint is equivalently converted into a convex form, and a real variable is used for carrying out lossless convexity on an event constraint function, so that the convergence and the efficiency of the spacecraft rendezvous and docking trajectory planning with the event constraint are improved on the premise of not changing the original problem solution space.
The purpose of the invention is realized by the following technical scheme:
the invention discloses a method for making a spacecraft rendezvous and docking trajectory planning event constraint convex, which comprises the steps of firstly selecting a variable search range containing an original optimal design variable solution space according to relevant design variables of an event constraint function, and carrying out grid discretization on the whole variable search space. And calculating the event function value at the boundary of each discretization grid according to the constraint function form. And obtaining a linear constraint function form inside the discretization grid by adopting low quadratic gravity center interpolation. Traversing calculation is carried out on all discretization grids in the search space, and constraint function values in the whole search space are converted into event constraints in a grid judgment constraint and linear interpolation mode. Subsequently, a series of real variables are introduced, and a volume detection method is adopted to adapt the new variables to describe the grid triggering condition in the search space. Real variables are introduced into the event constraint function through a relaxation-penalty mechanism, the convexity of grid judgment constraint is realized, and a linear event constraint expression form, namely a convex expression form of the event trigger function, is obtained on the premise of not introducing sequence approximation. And solving the convex expression form to obtain an optimal trajectory for rendezvous and docking of the spacecraft, so that the convergence and efficiency of planning the rendezvous and docking trajectory of the spacecraft with the event constraint are improved on the premise of not changing the original problem solution space.
The invention discloses a method for convexly constraining planning events of spacecraft rendezvous and docking trajectory, which comprises the following steps:
step one, discretizing an event constraint solution space to obtain a series of spatially discrete grids.
And defining a constraint function e (x) of the spacecraft trajectory planning event, wherein x is a relevant variable of the constraint of the spacecraft trajectory planning event. In the trajectory planning problem, the constraint function e (x) exists in the form as follows.
if p(x)＝0,then e(x)＝0
Wherein: p (x) represents the trigger function of the event constraint.
In the trajectory planning problem, when the condition p (x) is 0 is satisfied, meaning that the event is triggered, the event constraint condition e (x) needs to be satisfied; when the condition p (x) 0 is not satisfied, meaning that the event is not triggered, whether the event constraint condition e (x) 0 is satisfied or not does not affect the spacecraft trajectory.
Consider that x is a one-dimensional continuous design variable whose solution space is contained by the linear search space as follows.
Figure RE-GDA0003306696130000021
Where Ω denotes the solution space of the original event constraint function, xminMinimum search boundary, x, representing variable xmaxRepresenting the maximum search boundary for variable x.
Given a linear search space [ x ]min,xmax]The number n of discrete points of (c), the region omega is divided into a series of linear small grids, the small grids are expressed as omegaj
Ωj:＝[xmin,j,xmax,j]
Wherein: omegajRepresenting the jth linear small grid，xmin,jRepresents the lower bound, x, of the jth linear small gridmax,jRepresenting the upper bound of the jth linear small grid.
xmin,jAnd xmax,jSatisfies the following mathematical relationship
Figure RE-GDA0003306696130000022
Thus, the spatial grid is obtained, as well as the location parameters of the specific grid.
And step two, calculating a constraint function value at each discrete grid boundary point, and interpolating the constraint function data to obtain a linear expression form of the constraint function.
And calculating a constraint function value at the grid boundary in each given grid region according to the constraint function form.
el,j＝e(xmin,j)
eu,j＝e(xmax,j)
Wherein e isl,jRepresenting the value of a constraint function at the lower boundary of the jth linear small grid, eu,jThe constraint function values at the upper boundary of the jth linear small grid are represented.
Given linear small grid area
Ωj:＝[xmin,j,xmax,j]
And the value of the constraint function e in the regionl,jAnd eu,jObtaining the interpolation form of the constraint function in the region
Figure RE-GDA0003306696130000031
Thus, a linear event constraint function over the entire task area is obtained
Figure RE-GDA0003306696130000032
And step three, constructing an event detection function, relaxing the event constraint function, and performing convex grid judgment constraint to obtain a convex event constraint function form.
A relaxation variable k is introduced, which is a vector with dimension n-1. Using the relaxation variable to formulate an event-triggered constraint, define κjExpressing the jth component of the slack variable, the following inequality constraint is constructed
|x-xmin,j|+|x-xmax,j|≤κj
Meanwhile, a penalty term is additionally introduced into the performance index, so that the inequality constraint is obtained at any moment
Figure RE-GDA0003306696130000033
The event constraint function is mathematically transformed as follows
Figure RE-GDA0003306696130000034
Figure RE-GDA0003306696130000035
Where D represents a sufficiently large constant.
The constraint function has the following meaning when the variable x is located in the region
Figure RE-GDA0003306696130000041
When the lower bound of the relaxation factor is 0, i.e., κjWhen the value is 0, the event constraint function is equivalent to the original function; on the contrary, when the variable x is not located in the region
Figure RE-GDA0003306696130000042
And when the lower bound of the relaxation factor is larger than 0, the event constraint function is satisfied certainly, and the problem of trajectory planning is not solved.
And step four, constructing a switch function, describing the original event trigger function, and obtaining a convex expression form of the event trigger function.
For a given event trigger function p (x), the calculation is performed in each linear small region
Figure RE-GDA0003306696130000043
At the boundary, the value of the trigger function.
pl,j＝p(xmin,j)
pu,j＝p(xmax,j)
Wherein p isl,jExpressing the value of the event trigger function at the lower boundary of the jth linear small grid, pu,jIndicating the value of the event trigger function at the upper boundary of the jth linear small grid.
For the event-triggered constraint p (x) 0, using the zero theorem, one can obtain: current region
Figure RE-GDA0003306696130000044
When p (x) zero is present, there are
pl,j·pu,j≤0
Otherwise, there are
pl,j·pu,j＞0
Thus, a switching function ε is defined, which is expressed in the form of
if pl,j·pu,j≤0,ε＝0
if pl,j·pu,j＞0,ε＝1
Then, a switching function is introduced into the event detection function to obtain
ε(|x-xmin,j|+|x-xmax,j|)≤κj
Finally, a convex expression form of the event constraint function is obtained
Figure RE-GDA0003306696130000045
Subjectto
Figure RE-GDA0003306696130000046
Figure RE-GDA0003306696130000047
ε(|x-xmin,j|+|x-xmax,j|)≤κj
When the number of the spatial discrete points is large enough, the convex optimization problem is equivalent to the original problem, namely, the event constraint is equivalently converted into a convex form on the premise of not adopting a sequence approximation method.
Step five: solving the convex expression form in the step four to obtain an optimal rendezvous and docking trajectory of the spacecraft, and further improving the convergence and efficiency of planning the rendezvous and docking trajectory of the spacecraft with event constraints on the premise of not changing the original problem solution space.
Has the advantages that:
the invention discloses a method for making a spacecraft rendezvous and docking trajectory planning event constraint convex, which comprises the steps of firstly selecting a variable search range containing an original optimal design variable solution space according to relevant design variables of an event constraint function, and carrying out grid discretization on the whole variable search space. And calculating the event function value at the boundary of each discretization grid according to the constraint function form. And obtaining a linear constraint function form inside the discretization grid by adopting low quadratic gravity center interpolation. Traversing calculation is carried out on all discretization grids in the search space, and constraint function values in the whole search space are converted into event constraints in a grid judgment constraint and linear interpolation mode. Subsequently, a series of real variables are introduced, and a volume detection method is adopted to adapt the new variables to describe the grid triggering condition in the search space. And finally, introducing a real variable into an event constraint function through a relaxation-penalty mechanism, realizing the projection of grid judgment constraint, and avoiding the convergence and calculation speed loss caused by solving a trajectory planning problem in the traditional projection method. The method can improve the convergence and the calculation efficiency of the spacecraft rendezvous and docking trajectory planning with the event constraint on the premise of not changing the original problem solution space.
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FIG. 1 is a simulation diagram of spacecraft rendezvous and docking trajectory planning with event constraints.
Fig. 2 is a flowchart of a method for highlighting a spacecraft rendezvous and docking trajectory planning event constraint disclosed by the invention.
Detailed Description
For a better understanding of the objects and advantages of the present invention, reference should be made to the following detailed description taken in conjunction with the accompanying drawings and examples.
Example 1: projection of near-earth spacecraft rendezvous and docking trajectory planning problem
As shown in fig. 2, the method for convexly constraining the planning event constraint of the rendezvous and docking trajectory of the spacecraft disclosed in this embodiment includes the following specific steps
Step one, according to the problem definition, constructing an event constraint basic form, and selecting an event constraint solution space boundary.
Considering the rendezvous and docking process of two spacecrafts, the position vectors of the two spacecrafts are r respectively1And r2Defining the event trigger function as
p(r1,r2)＝∑|r1-r2|
Wherein, p (r)1,r2) Representing a spacecraft rendezvous docking event trigger function.
The trigger function means that when the positions of the two spacecrafts are consistent, the meeting and butt joint operation is judged to be needed; and if the positions are not consistent, the butting operation is not carried out.
Accordingly, an event constraint function is defined as e (m), which is embodied in the form of
e(m1,m2,m3)＝m1+m2-m3
Wherein m is1、m2Respectively representing the masses of two spacecrafts, m3Represents the total mass of two spacecrafts after meeting and docking, and the mass is a constant.
Thus, define m1、m2For event-constrained dependent variables, the solution space boundary is m1,min、m1,max、m2,min、 m2,maxWherein m is1,minIs a variable m1Minimum value of (1), m1,maxIs a variable m1Maximum value of (1), m2,minIs a variable m2Minimum value of (1), m2,maxIs a variable m2Is measured.
And step two, discretizing the event constraint solution space to obtain a series of spatially discrete grids.
Define the variable solution space as follows
Figure RE-GDA0003306696130000061
Where Ω represents the solution space of the original event constraint function.
Given a linear search space
Figure RE-GDA0003306696130000062
Number of discrete points n1Linear search space
Figure RE-GDA0003306696130000063
Number of discrete points n2The region Ω is divided into a series of linear small grids, denoted as Ωj
Ωj:＝[m1,min,j,m1,max,j]×[m2,min,j,m2,max,j]
Wherein: omegajDenotes the jth linear small grid, m1,min,jRepresents the variable m in the jth linear small grid1Lower boundary of (m)1,max,jRepresents the variable m in the jth linear small grid1Lower boundary of (m)2,min,jRepresents the variable m in the jth linear small grid2Lower boundary of (m)2,max,jRepresents the variable m in the jth linear small grid2The lower bound of (c).
And step three, calculating a constraint function value at each discrete grid boundary point.
Dividing a small square grid area into two triangular areas
Ωj -:＝Δ{(m1,min,j,m2,max,j),(m1,min,j,m2,min,j),(m1,max,j,m2,min,j)}
Ωj +:＝Δ{(m1,min,j,m2,max,j),(m1,max,j,m2,max,j),(m1,max,j,m2,min,j)}
Wherein omegaj -Is a lower triangle, omega, within a squarej +The operator Δ represents a triangular region composed of three feature points, which is an upper triangle inside a square.
According to the constraint function form, in each given grid region, a constraint function value at the grid boundary can be obtained through calculation, and three points in the grid are defined to be M respectively1、M2、M3And expressing the constraint function values corresponding to three points in the grid as e1、e2、e3。
And step four, interpolating the constraint function data to obtain a linear expression form of the constraint function.
Computing a constraint function interpolation form within the region
Figure RE-GDA0003306696130000064
Where the function S represents a linear function of the area of a triangle given its three vertices.
Thus, a linear event constraint function over the entire task area can be derived
if(m1,m2)∈[m1,min,j,m1,max,j]×[m2,min,j,m2,max,j]
Figure RE-GDA0003306696130000071
And fifthly, constructing an event detection function and describing the position of the event constraint related variable in a solution space.
A relaxation variable k is introduced, which is,the relaxation variable is a vector with dimension n-1. Using the relaxation variable to formulate an event-triggered constraint, define κjExpressing the jth component of the slack variable, the following inequality constraint is constructed
S{(m1,m2),M1,M2}+S{(m1,m2),M1,M3}+S{(m1,m2),M2,M3}≤κj
Meanwhile, a penalty term is additionally introduced into the performance index, so that the inequality constraint is obtained at any moment
Figure RE-GDA0003306696130000072
And step six, relaxing the event constraint function, and judging constraint by a convex grid to obtain a convex event constraint function form in the specific area.
The event constraint function is mathematically transformed as follows
Figure RE-GDA0003306696130000073
Figure RE-GDA0003306696130000074
Where D represents a sufficiently large constant.
The constraint function has the following meaning when the variable x is located in the region
Figure RE-GDA0003306696130000075
When the lower bound of the relaxation factor is 0, i.e., κjWhen the value is 0, the event constraint function is equivalent to the original function; on the contrary, when the variable x is not located in the region
Figure RE-GDA0003306696130000076
When the lower bound of the relaxation factor is larger than 0, the event constraint function is satisfied certainly, and the problem of trajectory planning is not solved。
And step seven, constructing a switch function and describing the original event trigger function.
Triggering a function p (r) for a given event1,r2) Calculating a trigger function value at each cell boundary, denoted as pll,j、pru,j、plu,j、prl,j. Wherein p isll,jExpressing the value of the event trigger function at the lower left boundary of the jth linear small grid, pru,jExpressing the value of the event trigger function at the upper right boundary of the jth linear small grid, plu,jExpressing the value of the event trigger function at the upper left boundary of the jth linear small grid, prl,jThe value of the event trigger function at the lower right boundary of the jth linear small grid is represented.
For event trigger constraint p (r)1,r2) With the zero theorem, 0, we can get: current region
Figure RE-GDA0003306696130000077
Presence of p (r)1,r2) At zero time, there are
pll,j·pru,j≤0
Otherwise, there are
pll,j·pru,j＞0
Thus, a switching function ε is defined, which is expressed in the form of
if pll,j·pru,j≤0,ε＝0
if pll,j·pru,j＞0,ε＝1
And step eight, constructing a convex event constraint form according to the switching function.
Introducing a switching function into the event detection function to obtain
ε(|x-xmin,j|+|x-xmax,j|)≤κj
Finally, a convex expression form of the event constraint function is obtained
Figure RE-GDA0003306696130000081
Subjectto
Figure RE-GDA0003306696130000082
Figure RE-GDA0003306696130000083
ε(S{(m1,m2),M1,M2}+S{(m1,m2),M1,M3}+S{(m1,m2),M2,M3})≤κj
The intersection butt joint trajectory obtained by adding the constraint obtained by the convex processing of the example to the spacecraft intersection butt joint trajectory planning problem is shown in fig. 1.
The above detailed description is intended to illustrate the objects, aspects and advantages of the present invention, and it should be understood that the above detailed description is only exemplary of the present invention and is not intended to limit the scope of the present invention, and any modifications, equivalents, improvements and the like made within the spirit and principle of the present invention should be included in the scope of the present invention.

Claims (6)

1. A method for making a spacecraft meet and butt joint a trajectory planning event constraint convex is characterized by comprising the following steps: comprises the following steps of (a) carrying out,
carrying out discretization processing on an event constraint solution space to obtain a series of spatially discrete grids;
calculating a constraint function value at each discrete grid boundary point, and interpolating constraint function data to obtain a linear expression form of the constraint function;
step three, constructing an event detection function, relaxing the event constraint function, and performing convex grid judgment constraint to obtain a convex event constraint function form;
and step four, constructing a switch function, describing the original event trigger function, and obtaining a convex expression form of the event trigger function.
2. The method of claim 1, wherein the method comprises: further comprises the following steps: solving the convex expression form in the step four to obtain an optimal rendezvous and docking trajectory of the spacecraft, and further improving the convergence and efficiency of planning the rendezvous and docking trajectory of the spacecraft with event constraints on the premise of not changing the original problem solution space.
3. A method of convexing constraints of a spacecraft rendezvous and docking trajectory planning event according to claim 1 or 2, wherein: the first implementation method comprises the following steps of,
defining a spacecraft trajectory planning event constraint function as e (x), wherein x is a relevant variable of the spacecraft trajectory planning event constraint; in the trajectory planning problem, the constraint function e (x) exists in the form of;
if p(x)＝0,then e(x)＝0
wherein: p (x) a trigger function representing an event constraint;
in the trajectory planning problem, when the condition p (x) is 0 is satisfied, meaning that the event is triggered, the event constraint condition e (x) needs to be satisfied; when the condition p (x) 0 is not satisfied, it means that the event is not triggered, and whether the event constraint condition e (x) 0 is satisfied or not does not affect the spacecraft trajectory;
considering x as a one-dimensional continuous design variable, the solution space of the variable is contained by the following linear search space;
Figure FDA0003232605470000011
where Ω denotes the solution space of the original event constraint function, xminMinimum search boundary, x, representing variable xmaxRepresents the maximum search boundary for variable x;
given a linear search space [ x ]min,xmax]The number n of discrete points divides the region omega into a series of linear small netsGrid, the small grid being denoted omegaj
Ωj:＝[xmin,j,xmax,j]
Wherein: omegajDenotes the jth linear small grid, xmin,jRepresents the lower bound, x, of the jth linear small gridmax,jAn upper bound representing the jth linear small grid;
xmin,jand xmax,jSatisfies the following mathematical relationship
Figure FDA0003232605470000012
Thus, the spatial grid is obtained, as well as the location parameters of the specific grid.
4. The method of claim 3, wherein the method comprises: the second step is realized by the method that,
according to the constraint function form, in each given grid area, calculating to obtain a constraint function value at the grid boundary;
el,j＝e(xmin,j)
eu,j＝e(xmax,j)
wherein e isl,jRepresenting the value of a constraint function at the lower boundary of the jth linear small grid, eu,jRepresenting a constraint function value at an upper boundary of a jth linear small grid;
given linear small grid area
Ωj:＝[xmin,j,xmax,j]
And the value of the constraint function e in the regionl,jAnd eu,jObtaining the interpolation form of the constraint function in the region
Figure FDA0003232605470000021
Thus, a linear event constraint function over the entire task area is obtained
Figure FDA0003232605470000022
5. The method of claim 4, wherein the method comprises: the third step is to realize the method as follows,
introducing a relaxation variable k, which is a vector with a dimension of n-1; using the relaxation variable to formulate an event-triggered constraint, define κjExpressing the jth component of the slack variable, the following inequality constraint is constructed
|x-xmin,j|+|x-xmax,j|≤κj
Meanwhile, a penalty term is additionally introduced into the performance index, so that the inequality constraint is obtained at any moment
Figure FDA0003232605470000023
The event constraint function is mathematically transformed as follows
Figure FDA0003232605470000024
Figure FDA0003232605470000025
Wherein D represents a sufficiently large constant;
the above constraint function has the following meaning when the variable x is located in the region xmin,j,xmax,j]When the lower bound of the relaxation factor is 0, i.e., κjWhen the value is 0, the event constraint function is equivalent to the original function; on the contrary, when the variable x is not located in the region [ x ]min,j,xmax,j]When the lower bound of the relaxation factor is larger than 0, the event constraint function must satisfyAnd the method does not enter the trajectory planning problem.
6. The method of claim 5, wherein the method comprises: the implementation method of the fourth step is that,
for a given event trigger function p (x), calculate in each linear small region [ x [ ]min,j,xmax,j]At the boundary, the value of the trigger function;
pl,j＝p(xmin,j)
pu,j＝p(xmax,j)
wherein p isl,jExpressing the value of the event trigger function at the lower boundary of the jth linear small grid, pu,jRepresenting the value of the event trigger function at the upper boundary of the jth linear small grid;
for the event-triggered constraint p (x) 0, using the zero theorem, one can obtain: when region [ xmin,j,xmax,j]When p (x) zero is present, there are
pl,j·pu,j≤0
Otherwise, there are
pl,j·pu,j＞0
Thus, a switching function ε is defined, which is expressed in the form of
if pl,j·pu,j≤0,ε＝0
if pl,j·pu,j＞0,ε＝1
Then, a switching function is introduced into the event detection function to obtain
ε(|x-xmin,j|+|x-xmax,j|)≤κj
Finally, a convex expression form of the event constraint function is obtained
Figure FDA0003232605470000031
Subject to
Figure FDA0003232605470000032
Figure FDA0003232605470000033
ε(|x-xmin,j|+|x-xmax,j|)≤κj
When the number of the spatial discrete points is large enough, the convex optimization problem is equivalent to the original problem, namely, the event constraint is equivalently converted into a convex form on the premise of not adopting a sequence approximation method.
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Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114859974A (en) * 2022-05-19 2022-08-05 浙江大学 Full-flow continuous trajectory planning method and system for spacecraft approach rendezvous maneuver
CN114955009A (en) * 2022-05-20 2022-08-30 北京航天飞行控制中心 Selection method, system, medium and equipment of earth orbit intersection butt joint
CN116692030A (en) * 2023-06-01 2023-09-05 四川大学 Spacecraft redirection control method based on event triggering mechanism

Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20100108819A1 (en) * 2005-07-20 2010-05-06 Junichiro Kawaguchi Method for designing an orbit of a spacecraft
WO2017005052A1 (en) * 2015-07-09 2017-01-12 北京航空航天大学 Optimization and design method for gradient segmentation of intervals of spacecraft pulse rendezvous trajectory
CN111486851A (en) * 2020-04-27 2020-08-04 中国人民解放军国防科技大学 Method and device for planning short-distance relative motion three-dimensional obstacle avoidance track of spacecraft
CN112051854A (en) * 2020-09-23 2020-12-08 北京理工大学 Rapid planning method for optimal trajectory of lunar soft landing considering complex constraints

Patent Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20100108819A1 (en) * 2005-07-20 2010-05-06 Junichiro Kawaguchi Method for designing an orbit of a spacecraft
WO2017005052A1 (en) * 2015-07-09 2017-01-12 北京航空航天大学 Optimization and design method for gradient segmentation of intervals of spacecraft pulse rendezvous trajectory
CN111486851A (en) * 2020-04-27 2020-08-04 中国人民解放军国防科技大学 Method and device for planning short-distance relative motion three-dimensional obstacle avoidance track of spacecraft
CN112051854A (en) * 2020-09-23 2020-12-08 北京理工大学 Rapid planning method for optimal trajectory of lunar soft landing considering complex constraints

Non-Patent Citations (2)

* Cited by examiner, † Cited by third party
Title
PINGYUAN CUI, TONG QIN, SHENGYING ZHU, YANG LIU, RUI XU, ZHENGSHI YU: "Trajectory curvature guidance for Mars landings in hazardous terrains", AUTOMATICA, vol. 93, pages 161 - 171 *
池贤彬;岳晓奎;李鹏;: "基于凸优化的自主交会迭代制导方法", 中国空间科学技术, no. 01, pages 26 - 34 *

Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114859974A (en) * 2022-05-19 2022-08-05 浙江大学 Full-flow continuous trajectory planning method and system for spacecraft approach rendezvous maneuver
CN114955009A (en) * 2022-05-20 2022-08-30 北京航天飞行控制中心 Selection method, system, medium and equipment of earth orbit intersection butt joint
CN116692030A (en) * 2023-06-01 2023-09-05 四川大学 Spacecraft redirection control method based on event triggering mechanism
CN116692030B (en) * 2023-06-01 2024-02-09 四川大学 Spacecraft redirection control method based on event triggering mechanism

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