CN117262252B - Spacecraft autonomous intersection and docking control method capable of realizing fuel optimization - Google Patents
Spacecraft autonomous intersection and docking control method capable of realizing fuel optimization Download PDFInfo
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Abstract
The invention discloses a spacecraft autonomous rendezvous and docking control method capable of realizing fuel optimization, which comprises the following steps: step 1, considering the problem of intersection and butt joint of the motion of a tracking spacecraft on a near-circular orbit, and establishing a relative motion dynamics equation of the spacecraft based on a CW equation; step 2, a target port motion model is established by considering slow rotation of a target spacecraft; step 3, establishing corresponding task constraint aiming at various task requirements in the autonomous meeting and docking process of the spacecraft; step 4, optimizing the sight cone constraint established in the step 3; step 5, designing a convergence butt joint controller based on variable range model predictive control, and establishing a related optimal control problem; and step 6, providing a solving strategy of the optimal control problem in the variable range model predictive control under the meeting butt joint task scene. The invention directly and effectively solves the problem of fuel optimization in the process of intersection and butt joint.
Description
Technical Field
The invention belongs to the field of linear system control, relates to a spacecraft autonomous rendezvous and docking control algorithm, and in particular relates to a spacecraft autonomous rendezvous and docking control method capable of realizing fuel optimization.
Background
The task scene of autonomous rendezvous and docking is a three-dimensional universe space; the task requirements can ensure that the tracking spacecraft reaches the position of the designated docking port, and meanwhile, the inherent performance limit of the spacecraft propellers, the path constraint in the intersecting process, the geometric shape of the target spacecraft and the relative speed between the spacecraft during docking are considered. In order to improve the robustness of the mission, the problem that the target spacecraft slightly rotates is also considered. In addition, as reasonable load of the spacecraft is a premise of completing the whole exploration task, fuel consumption in the process of intersection and butt joint should be optimized, and therefore feasibility of the whole task is improved.
The model predictive control has the characteristic of dynamic re-planning, not only can ensure the state convergence of the controlled object, but also can ensure that the controlled object meets various complex constraint problems including path constraint. And, because the model predictive control is based on solving a certain pre-designed optimal control problem to perform controller calculation, the model predictive control provides a solution to the fuel optimization problem in the process of intersection and docking.
Disclosure of Invention
The invention aims to provide a spacecraft autonomous rendezvous and docking control method capable of realizing fuel optimization, which adopts a spacecraft relative motion dynamics model expressed by a CW equation, considers various task constraints in autonomous rendezvous and docking and task requirements of fuel optimization, designs a docking algorithm based on variable range model predictive control, and further provides a quick and efficient solving strategy of the control algorithm under the task scene to realize the rendezvous and docking control of a spacecraft.
The invention aims at realizing the following technical scheme:
a spacecraft autonomous rendezvous and docking control method capable of realizing fuel optimization comprises the following steps:
Step 1, considering the problem of intersection and butt joint of motion of a tracking spacecraft on a near-circular orbit, and establishing the following spacecraft relative motion dynamics equation based on a CW equation in a local vertical/local horizontal coordinate system established according to the tracking spacecraft:
Wherein F x,Fy,Fz is the thrust component of the tracking spacecraft in the x, y and z directions respectively; u x,uy,uz denotes the x, y, z direction control components; m c represents tracking spacecraft mass; n represents the track rate;
step 2, considering slow rotation of the target spacecraft, and establishing a target port motion model as follows:
Wherein, Represents the relative position, relative speed/>, of the docking port at any momentRepresenting the relative speed of the docking port at any moment; ω (t) represents the target spacecraft port real-time angular velocity;
obtaining the state vector of the butt joint point by sampling p d、vd
Wherein,Respectively representing the relative position and the relative speed of the port at the moment k, wherein τ s represents the sampling period;
Step 3, establishing corresponding task constraint aiming at various task requirements in the autonomous meeting and docking process of the spacecraft, wherein:
The thrust constraint is:
||U||∞≤umax；
wherein u max is the maximum acceleration which can be output in a single direction of the tracking spacecraft;
the soft docking constraint is:
the sight cone constraint is:
wherein alpha represents the half angle of the cone, Representing the unit direction vector of the butt joint shaft;
and 4, optimizing the sight cone constraint established in the step 3, wherein the optimized sight cone expression is as follows:
Step 5, designing a convergence butt joint controller based on variable range model predictive control aiming at the motion models and various constraints designed in the step 1, the step 2, the step 3 and the step 4, and establishing related optimal control problems, wherein the optimal control problems are as follows:
Wherein, gamma > 0 represents the fuel consumption term weight, Representing a natural number set, wherein N represents a prediction range;
Step 6, aiming at the step 5, a solution strategy of an optimal control problem in the prediction control of the variable range model under the scene of the meeting butt joint task is provided, wherein the solution strategy is as follows: at any sampling time in the control process, the upper and lower boundaries of a search interval for solving the optimal control problem are contracted, and the optimal control problem is solved by using a golden section search method based on the contracted interval, wherein:
lower bound shrinkage takes the form:
the upper bound shrinkage is of the form:
compared with the prior art, the invention has the following advantages:
The invention designs a controller based on variable range model predictive control aiming at the problem of autonomous rendezvous and docking of a spacecraft. The controller can ensure that the tracking spacecraft and the target spacecraft with the rotating docking port finish the rendezvous docking, and meet various task constraints in the task process. And the path constraint in the intersecting process is further optimized, so that the solving speed of the optimization solver is improved. Meanwhile, the controller meets the requirements of recursive feasibility and limited time accessibility, ensures that the controller is always effective in the task process, and ensures that the controlled object can reach the expected state. Aiming at the task scene related by the invention, an optimal problem solving strategy based on search interval contraction and golden section search method is provided, and the efficient and accurate solving of the optimal control problem in the controller is realized. The invention directly and effectively solves the problem of fuel optimization in the process of intersection and butt joint.
Drawings
FIG. 1 is a schematic diagram of autonomous cross docking control of a spacecraft;
FIG. 2 is a schematic diagram of relative movement of a spacecraft;
FIG. 3 is a schematic view of a rotating cone of sight constraint;
FIG. 4 is a schematic illustration of a constrained contraction effect;
FIG. 5 is a block diagram of a model predictive control system;
FIG. 6 is a diagram of A curve varying with N;
FIG. 7 is a flow chart of the golden section search method;
FIG. 8 is an illustration of the optimal cost for different algorithms and their counterparts;
FIG. 9 is a diagram showing various algorithms and their corresponding search times;
FIG. 10 is a graph showing the change in position and relative position in the x-direction during mating;
FIG. 11 is a graph showing the change in position and relative position in the y-direction during mating;
FIG. 12 is a graph showing the change in position and relative position in the z-direction during mating;
FIG. 13 is a graph showing the change in velocity and relative velocity in the x-direction during mating;
FIG. 14 is a graph showing the velocity and relative velocity in the y-direction during mating;
FIG. 15 is a graph showing the change in velocity and relative velocity in the z-direction during mating;
FIG. 16 is a control output during a mating phase;
fig. 17 is a schematic view of three-dimensional motion of the convergence butt joint.
Detailed Description
The following description of the present invention is provided with reference to the accompanying drawings, but is not limited to the following description, and any modifications or equivalent substitutions of the present invention should be included in the scope of the present invention without departing from the spirit and scope of the present invention.
The invention provides a spacecraft autonomous rendezvous and docking control method capable of realizing fuel optimization, which adopts a CW equation to establish a spacecraft relative motion dynamics equation, considers slow rotation of a target spacecraft in a three-dimensional space environment, designs a controller based on variable range model predictive control, further optimizes the controller, and proposes a solving strategy of an optimal control problem in the controller, thereby realizing the autonomous rendezvous and docking control of the spacecraft on the premise of meeting various task requirements, and simultaneously optimizing fuel consumption in the rendezvous and docking process. As shown in fig. 1, the method specifically comprises the following steps:
Step 1, considering the problem of intersection and butt joint of motion of a tracked spacecraft on a nearly circular orbit, and establishing a relative motion dynamics equation of the spacecraft based on a CW equation according to a local vertical/local horizontal coordinate system established by the tracked spacecraft, wherein the specific form is as follows:
Wherein F x,Fy,Fz is the thrust component of the tracking spacecraft in the x, y and z directions respectively; u x,uy,uz denotes the x, y, z direction control components; m c represents tracking spacecraft mass; n represents the track rate.
The state space is given as follows:
Wherein, Is a state vector,/>Representing a control vector, X p representing a position component; x v represents a velocity component.
Since model predictive control is a discrete control method, discretization processing is also required for the continuous system model:
where τ s represents the sampling period.
Step2, considering slow rotation of the target spacecraft, and building a target port motion model, wherein the specific form is as follows:
Wherein, Represents the relative position, relative speed/>, of the docking port at any momentThe relative speed of the butt joint port at any moment is represented, and omega (t) represents the real-time angular speed of the port of the target spacecraft.
State vector of butt joint pointCan be obtained by directly sampling p d,vd:
Wherein, Representing the relative position and relative speed of the port at time k, respectively.
Step 3, establishing corresponding task constraint aiming at various task requirements in the autonomous meeting and docking process of the spacecraft, wherein:
The thrust constraint is:
||U||∞≤umax
wherein u max is the maximum acceleration which can be output in a single direction of the tracking spacecraft;
the soft docking constraint is:
Sight cone constraint The method comprises the following steps:
wherein alpha represents the half angle of the cone, Representing the unit direction vector of the butt joint axis.
The following control constraint sets are respectively given for the task constraintsAnd state constraint set/>
And 4, optimizing the sight cone constraint established in the step 3, so that the complexity of the optimization problem is reduced, and the solving speed is improved.
First a rotation matrix R (k) is selected as follows:
Wherein, A rotation matrix defined for the angle-axis representation represents an arbitrary three-dimensional vector rotated by an angle of θ degrees about a unit direction vector v= [ xyz ] T. Therefore, the rotation matrix R (k) represents the butt axis direction vector/>After the rotation conversion, the unit vector e 1＝[1 0 0]T on the x-axis is converted. According to the geometric relationship, each space vector satisfies the following equation:
Consider the following equation:
Meanwhile, according to the rotation matrix R (k), the following expression can be obtained:
R(k)TR(k)＝I
according to the following formulas:
Since e 1 is a unit basis vector, the vector At most two non-zero elements are contained. Based on the conclusion and the norm inequality, the original sight cone constraint/>Shrinkage intoThe following is shown:
Since the left side inequality is equivalent to:
the right side inequality is therefore equally valid as the above form, and therefore, a new set of constraints Is a standard form of polyhedral set, namely, is equivalent to shrinking the original cone domain into the polyhedral domain, so that the secondary constraint is optimized to be the primary constraint, and the schematic diagrams before and after shrinkage are shown in fig. 4.
And 5, designing an intersection butt joint controller based on variable range model predictive control aiming at the motion models and various constraints designed in the step 1, the step 2, the step 3 and the step 4, and establishing a related optimal control problem, wherein a control system block diagram is shown in fig. 5. The design optimal control problem is as follows:
s.t.X(j+1|k)＝AdX(j|k)+BdU(j|k),j＝0,...,N-1
X(0|k)＝X(k)
X(N|k)＝Xd(k+N)
Wherein, gamma > 0 represents the fuel consumption term weight, Representing a natural number set; n represents the prediction horizon. A set of possible control sequences and possible state sequences for the above-mentioned optimal control problem are denoted by U (k), X (k), respectively, which consist of:
The optimal cost, optimal control sequence, and optimal state trajectory determined by solving the above-described optimal control problem at time k are denoted by J *(k)、U*(k)、X* (k), respectively. The control input U * (k) at time k is thus obtained as:
U*(k)＝[100…]U*(k)
And step 6, aiming at the step 5, a solving strategy of the optimal control problem in the variable range model predictive control under the meeting butt joint task scene is provided. The solution strategy is: and at any sampling time in the control process, the upper and lower boundaries of the search interval for solving the optimal control problem are contracted, and the golden section search method is used for solving the optimal control problem based on the contracted interval.
Consider the following second order cone programming problem:
s.t.X(j+1|k)＝AdX(j|k)+BdU(j|k),j＝0,...,N-1
X(0|k)＝X(k)
X(N|k)＝Xd(k+N)
in this problem, the prediction horizon N is a fixed, known parameter. Such a problem facilitates solving its optimal control sequence U * and corresponding optimal cost If the problem is not viable, then consider/>This problem can be regarded as a function map/>Thus the solution of the optimal control problem in step 5 can be equivalent to solving/>Is obtained. Function definition field is/>Where N ub represents the maximum prediction horizon of the original problem. The search interval is then contracted to reduce the complexity of solving the equivalence problem.
Contracting the search interval upper bound:
assume the optimal control problem in step 5 There is a set of optimal solutions at time k 0:
A set of possible solutions to the optimization problem at time k 0 +1 can be constructed as:
hence the problem at time k 0 Optimal cost of (1) and k 0 +1 time problem/>The feasible costs of (1) are respectively:
According to the 1-norm definition, the two-time control sequence satisfies the following inequality:
||U(k0+1)||1＜||U*(k0)||1
the corresponding costs at two moments therefore satisfy:
For the optimal control problem, the optimal cost at any moment is less than or equal to any feasible cost, so that the optimal cost at two adjacent moments meets the following conditions:
Thus, for any time k, the problem Optimal prediction Range/>The method meets the following conditions:
Thus, problems The upper bound N max of the search interval of (a) satisfies:
Contracting the search interval lower bound:
Consider an arbitrary linear discrete system X (k+1) =ax (k) +bu (k), assuming that the system can reach the target state X d(k0 +n from the initial state X (k 0)＝X0). The N-step energy matrix is defined as R N＝[AN-1 b. Consider its energy optimal control problem:
min‖UN‖2
s.t.X(0|k0)＝X(k0)
X(j+1|k)＝AX(j|k)+BU(j|k)
X(N|k0)＝Xd(N|k0)
this problem is equivalent to solving:
min‖UN‖2
s.t.Xd(k0+N)＝ANX0+RNUN
Thus, for any linear discrete system, its unconstrained minimum energy control sequence is Wherein/>Representing the pseudo-inverse of R N. The following feasibility problems are considered next:
find UN
s.t.X(0|k)＝X(k)
X(j+1|k)＝AX(j|k)+BU(j|k)
||UN||∞≤1
X(N|k)＝Xd(N|k)
Since e N is the minimum energy control sequence that causes the system to transition from the initial state X 0 to the target state X d(k0 +n), for any control sequence U N, the following inequality relationship can be derived from the norm inequality:
Only when When the constraint U N||∞ is smaller than or equal to 1, the constraint U N||∞ is satisfied. Thus, the feasibility problem only holds when the search interval satisfies the following set:
thus, the interval The lower bound N min of (1) is the problem/>Is a lower bound of the search interval of (c).
To sum up, at any moment, the problemSearch space/>From { 1..N ub } to { N min,...,Nmax }.
Golden section search method:
Solving the non-convex optimization problem at any moment Conversion to in-interval/>Searching for unimodal function map/>Is a minimum of (2). /(I)The curves as N are shown in FIG. 6, it can be seen that/>Because of the mapping of the unimodal function, the invention adopts the golden section searching method to complete the one-dimensional searching task. A flowchart of the golden section search is shown in fig. 7.
The parameters required in the process of meeting and docking are as follows:
initial docking port state: x d(0)＝[200 -20 15 0.01 0 0]T m
Initial tracking of spacecraft state: x (0) = [ 5000 0.05-0.05 ] T m
Target port angular velocity: omega (t) = [ 0.003.01.0.01 ] T rad s
Sampling interval: τ s =2s
Conical half angle: alpha=20 deg
Maximum acceleration: u max＝0.2m/s2
Track rate: n=1.107×10 -3 rad/s
Weight of fuel consumption term: gamma=2
Maximum prediction range: n ub = 125
In order to compare the solving effects of the interval contraction and golden section searching method, the designated initial value searching method and the global searching method, 1000 initial docking positions of tracking spacecrafts are randomly generated within a sight cone range of 30 m-300 m from a target port so as to perform Monte Carlo simulation. To facilitate the demonstration of the simulation effect, the initial velocity of the tracking spacecraft is set to 0. The results of the Monte Carlo simulation are shown in FIGS. 8-9.
Fig. 8 shows the results of the solutions of the three algorithms in the same case. The method can obtain the same solving result as the other two methods, and the method can accurately solve the non-convex optimal control problem in the VHMPC controller.
Fig. 9 shows the number of convex optimization solutions that need to be performed to solve the non-convex optimization problem when three methods solve the same case. Compared with the global search and the designated initial value search method, the algorithm provided by the invention only needs to search for a plurality of bits in each sampling time, so that the solving cost of the original problem is obviously reduced, and the solving efficiency is improved.
In the process of meeting and docking, the space position of the spacecraft and the space position of the docking port are tracked, and the relative position of the spacecraft after the spacecraft reaches the vicinity of the docking point is tracked, as shown in fig. 10 to 12. From the figure, the tracking spacecraft reaches the rotating butt joint port for 66s or so, and the tracking error of the position is kept within 10 -2 orders of magnitude, so that the position requirement in the butt joint task is met.
In the process of meeting and docking, the speed of the spacecraft and the docking port are tracked, and the relative speed change of the spacecraft after reaching the vicinity of the docking point is tracked as shown in fig. 13-15. It can be seen that when the tracking spacecraft arrives near the docking port, the speed of the tracking spacecraft and the speed of the docking port can be kept consistent, the tracking error of the speed is kept within 10 -3 orders of magnitude, and the soft docking task requirement in the docking task is met.
The control input condition in the process of intersection and butt joint is shown in fig. 16, and in the process of task duration, the control input is always kept in the required value range, so that the control constraint is met.
The situation of the intersecting and docking motion based on VHMPC controllers is shown in fig. 17, and the tracking spacecraft is always kept in the sight cone of the docking port in the task duration process, so that the task-related path constraint is met.
To verify VHMPC the fuel optimizing effect of the controller on the docking task, simulations were performed under different fuel consumption term weights γ, respectively, and the time t d required for docking and the fuel consumption J required for docking process under the corresponding weights were given as shown in table 1. As can be seen from comparison of the crossing docking time and the fuel consumption of the LQMPC controller, the fuel consumption of the VHMPC controller is only 7.4859m/s 2 under the similar docking time, and the optimization effect can reach at least 45%. Meanwhile, as the weight term increases, the docking time increases, the fuel consumption decreases, and each numerical value shows linear change. Compared with LQMPC controllers, the method has the advantages that the selection of parameters is clearer and simpler, and the optimization requirement of fuel consumption is effectively met.
Table 1 VHMPC Butt times and fuel consumption of the controller at different fuel consumption weights
。/>
Claims (2)
1. The spacecraft autonomous rendezvous and docking control method capable of realizing fuel optimization is characterized by comprising the following steps of:
Step 1, considering the problem of intersection and butt joint of motion of a tracking spacecraft on a near-circular orbit, and establishing the following spacecraft relative motion dynamics equation based on a CW equation in a local vertical/local horizontal coordinate system established according to the tracking spacecraft:
Wherein F x,Fy,Fz is the thrust component of the tracking spacecraft in the x, y and z directions respectively; u x,uy,uz denotes the x, y, z direction control components; m c represents tracking spacecraft mass; n represents the track rate;
step 2, considering slow rotation of the target spacecraft, and establishing a target port motion model as follows:
Wherein, Represents the relative position, relative speed/>, of the docking port at any momentRepresenting the relative speed of the docking port at any moment; ω (t) represents the target spacecraft port real-time angular velocity;
obtaining the state vector of the butt joint point by sampling p d、vd
Wherein,Respectively representing the relative position and the relative speed of the port at the moment k, wherein τ s represents the sampling period;
Step 3, establishing corresponding task constraint aiming at various task requirements in the autonomous meeting and docking process of the spacecraft, wherein:
The thrust constraint is:
||U||∞≤umax；
wherein u max is the maximum acceleration which can be output in a single direction of the tracking spacecraft;
the soft docking constraint is:
the sight cone constraint is:
wherein alpha represents the half angle of the cone, Representing the unit direction vector of the butt joint shaft;
and 4, optimizing the sight cone constraint established in the step 3, wherein the optimized sight cone expression is as follows:
wherein R (k) is a rotation matrix;
Step 5, designing a convergence butt joint controller based on variable range model predictive control aiming at the motion models and various constraints designed in the step 1, the step 2, the step 3 and the step 4, and establishing related optimal control problems, wherein the optimal control problems are as follows:
Wherein, gamma > 0 represents the fuel consumption term weight, Representing a natural number set, wherein N represents a prediction range;
step 6, aiming at the step 5, a solution strategy of an optimal control problem in the prediction control of the variable range model under the scene of the meeting butt joint task is provided, wherein the solution strategy is as follows: and at any sampling time in the control process, the upper and lower boundaries of the search interval for solving the optimal control problem are contracted, and the golden section search method is used for solving the optimal control problem based on the contracted interval.
2. The method for controlling autonomous rendezvous and docking of spacecraft capable of optimizing fuel according to claim 1, wherein in step 6, the lower bound shrinkage is as follows:
the upper bound shrinkage is of the form:
Wherein R N is an N-step energy matrix, e N is a minimum energy control sequence for transferring the system from an initial state X 0 to a target state X d(k0 +N), and N max is a problem N ub represents the maximum predicted range of the original problem.
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| CN105005651A (en) * | 2015-07-09 | 2015-10-28 | 北京航空航天大学 | Gradient separate zone optimization design method for spacecraft pulse rendezvous trajectory |
| CN109828464A (en) * | 2019-02-28 | 2019-05-31 | 北京控制工程研究所 | A kind of spacecraft Autonomous attitude control method |
| CN115524969A (en) * | 2022-09-26 | 2022-12-27 | 西北工业大学 | Method for improving prediction control operation speed of space intersection butt joint model |
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| CN105005651A (en) * | 2015-07-09 | 2015-10-28 | 北京航空航天大学 | Gradient separate zone optimization design method for spacecraft pulse rendezvous trajectory |
| 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 |
| CN109828464A (en) * | 2019-02-28 | 2019-05-31 | 北京控制工程研究所 | A kind of spacecraft Autonomous attitude control method |
| CN115524969A (en) * | 2022-09-26 | 2022-12-27 | 西北工业大学 | Method for improving prediction control operation speed of space intersection butt joint model |
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