CN112693631A - Initial trajectory generation method and system for aircraft in online sequence convex optimization - Google Patents

Initial trajectory generation method and system for aircraft in online sequence convex optimization Download PDF

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CN112693631A
CN112693631A CN202011352629.4A CN202011352629A CN112693631A CN 112693631 A CN112693631 A CN 112693631A CN 202011352629 A CN202011352629 A CN 202011352629A CN 112693631 A CN112693631 A CN 112693631A
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CN112693631B (en
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周祥
何睿智
谢磊
张洪波
汤国建
郑伟
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National University of Defense Technology
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B64—AIRCRAFT; AVIATION; COSMONAUTICS
    • B64G—COSMONAUTICS; VEHICLES OR EQUIPMENT THEREFOR
    • B64G1/00—Cosmonautic vehicles
    • B64G1/22—Parts of, or equipment specially adapted for fitting in or to, cosmonautic vehicles
    • B64G1/24—Guiding or controlling apparatus, e.g. for attitude control
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Abstract

The invention discloses an initial trajectory generation method and system in aircraft online sequence convex optimization, aiming at the problem of guidance of a first-level recovery landing segment of a carrier rocket, firstly, generating an initial trajectory of a first planning period based on the number of fixed discrete points; secondly, determining a time range of online sequence convex optimization of the current planning cycle, including initial time and terminal time, and discretizing the time range; if the previous planning period can obtain an effective reference track, performing linear interpolation on the reference track; otherwise, carrying out linear interpolation on the reference track of the last but one planning cycle so as to obtain the state quantity of each discrete point in the time range; and finally, forming an initial track for online sequential convex optimization in the current planning period based on the state quantities at the discrete points. The method can effectively solve the problem of low convergence speed of the online sequence convex optimization algorithm caused by large initial track error.

Description

Initial trajectory generation method and system for aircraft in online sequence convex optimization
Technical Field
The invention relates to the technical field of aircraft guidance control, in particular to an initial trajectory generation method and system in online sequence convex optimization.
Background
The carrier rocket sublevel recovery technology is one of key technologies for realizing the reusability of an engine and reducing the space entering cost. The vertical landing section is the last stage of the recovery process, and the vertical landing section adopts a variable thrust engine to control so as to realize rocket fixed-point landing, which puts higher requirements on the robustness and reliability of the guidance method. The current successful guidance scheme is a guidance method based on reference track on-line generation, the method carries out on-line generation of the reference track according to the current state in each planning period, the adaptability to interference factors is wider, and the robustness of the guidance method is improved. The core of the guidance method is the online generation of the reference track, the current track planning method with online application potential mainly is a sequence convex method, the method makes full use of the rapidity of solving a convex optimization problem, and the reference track is planned online based on the current state under the conditions of a given initial track, the number of discrete points and the like. The selection of the initial track directly influences the convergence speed and precision of sequence convexity, thereby influencing the updating frequency and precision of the reference track, and finally reflecting the influence on the performance of the guidance method. The traditional initial trajectory is obtained on the basis of linear hypothesis, namely, all motion state quantities are considered to be linearly changed, and the initial trajectory obtained by the method does not meet the dynamic constraint and has larger deviation with a real trajectory, so that the convergence speed of the sequence convexity is lower, even is not converged.
Disclosure of Invention
The invention aims to solve the technical problem that aiming at the defects of the prior art, the invention provides the initial track generation method and the system in the online sequence convex optimization, solves the problem that the initial track generation method based on the linear hypothesis easily causes the slow convergence speed of the sequence convex and even does not converge, and realizes the rapid convergence of the online sequence convex.
In order to solve the technical problems, the technical scheme adopted by the invention is as follows: an initial trajectory generation method in online sequential convex optimization of an aircraft comprises the following steps:
in a first planning period, generating an initial track by adopting a linear hypothesis method;
starting from the second planning period, determining the initial track used for online sequence convex optimization in the current period based on the reference track successfully planned last time.
The invention provides an initial track generation method in online sequence convex optimization. The method effectively improves the precision of generating the initial track in the subsequent planning period, reduces the number of sequence convex iteration times, improves the convergence speed, and simultaneously ensures the guidance precision.
In a first planning period, a specific implementation process for generating an initial trajectory by adopting a linear hypothesis method includes:
set from the current state
Figure BDA0002801761990000021
To terminal state SfIs linearly changed with time from the current state
Figure BDA0002801761990000022
To terminal state SfTime range of
Figure BDA0002801761990000023
Each uniformly discrete time is
Figure BDA0002801761990000024
The superscript 1 represents the 1 st planning cycle, the subscript represents the discrete time sequence number, N is the number of discrete points, then the initial trajectory of the current planning cycle is
Figure BDA0002801761990000025
Let the sequence number k of the planning period be 1, wherein
Figure BDA0002801761990000026
The values of the x-direction component of the position at different discrete times,
Figure BDA0002801761990000027
for the values of the y-direction component of the position at different discrete times,
Figure BDA0002801761990000028
the values of the z-direction component of the position at different discrete times,
Figure BDA0002801761990000029
the values of the velocity x-direction component at different discrete times,
Figure BDA00028017619900000210
for the values of the velocity y-direction component at different discrete times,
Figure BDA00028017619900000211
the subscripts of the position component and the velocity component represent the serial numbers of the discrete points,
Figure BDA00028017619900000212
current state
Figure BDA00028017619900000213
Terminal state Sf＝[0 0 0 0 0 0]Τ. The initial trajectory generation method adopting the linear hypothesis has the advantages of simple engineering realization, small calculation amount and the like.
Figure BDA00028017619900000214
The value is 0, and the dynamic characteristic analysis of the rocket sublevel recovery vertical landing section is carried out to obtain the target
Figure BDA00028017619900000215
The value range is set to be 20-60s, and the largest part of the flight time of the landing segment can be contained, so that the feasible reference track can be successfully planned through an online sequence convex optimization algorithm.
The implementation process of determining the initial track used for online sequence convex optimization in the current period based on the reference track successfully planned last time from the second planning period comprises the following steps: determining initial time and terminal time for performing online sequence convex optimization in the current planning period, and discretizing the time range; if the previous planning period obtains an effective reference track, performing linear interpolation on the reference track; otherwise, carrying out linear interpolation by using the reference track of the last but one planning cycle so as to obtain the state quantity of each discrete point in the time range; and the state quantities at the discrete points form an initial track for performing online sequential convex optimization in the current planning period. The problem of low convergence speed of online sequence convex optimization caused by large initial track error is further effectively solved.
The specific implementation process of acquiring the state quantity at the discrete point comprises the following steps:
1) based on an initialization trajectory
Figure BDA0002801761990000031
Executing an online sequence convex optimization algorithm, and outputting a reference track R obtained in the kth planning cycle after the algorithm is converged(k)Laying a foundation for the initial track generation of the next planning period;
2) the current motion state is obtained by measurement
Figure BDA0002801761990000032
Will be provided with
Figure BDA0002801761990000033
As an initial time of the (k + 1) th planning cycle, and
Figure BDA0002801761990000034
Tplanningto representPlanning cycle, movement state
Figure BDA0002801761990000035
As the initial state of the (k + 1) th planning period, providing an initial value for the (k + 1) th planning period to execute an online sequence convex optimization algorithm;
3) when in use
Figure BDA0002801761990000036
When so, ending; otherwise, turning to the step 4); wherein epsilonHJudging the tolerance for the landing condition; the step is used for judging whether the on-line track planning is terminated;
4) to be provided with
Figure BDA0002801761990000037
The time range for carrying out online sequence convex processing on the k +1 th planning period is equally divided into N-1 intervals to obtain corresponding moments at each discrete point in the time range, and the corresponding moments are recorded as
Figure BDA0002801761990000038
And is
Figure BDA0002801761990000039
The step realizes the discretization of the continuous problem and is the basis for executing the online sequence convex optimization algorithm;
5) if the reference track R is obtained in the k-th track planning period(k)If the path is not empty, namely the path planning is successful, executing step 6); otherwise, turning to step 7); the step considers different initial track generation strategies under two conditions, and different steps are subsequently executed for different strategies;
6) reference trajectory obtained based on kth planning cycle
Figure BDA00028017619900000310
Linear interpolation is performed to obtain a reference trajectory R(k)At each discrete time
Figure BDA00028017619900000311
Is taken as
Figure BDA0002801761990000041
Will be provided with
Figure BDA0002801761990000042
Taking the k +1 th planning period as an initialization track for online sequence projection, adding 1 to the value of k, and turning to the step 1); the step obtains a higher-precision initialization track by performing linear interpolation on the reference track obtained in the last planning cycle, and improves the convergence speed of the online sequence convex optimization algorithm;
7) reference track obtained based on k-1 planning cycle
Figure BDA0002801761990000043
Performing linear interpolation to obtain R(k-1)At each discrete time
Figure BDA0002801761990000044
Is taken as
Figure BDA0002801761990000045
Will be provided with
Figure BDA0002801761990000046
And (4) taking the initial trajectory as the k +1 th planning period for online sequence convex, adding 1 to the value of k, and turning to the step 1).
εHThe allowable value of the landing height is expressed in a physical sense, strictly speaking, 0 should be taken, but considering that certain deviation necessarily exists in algorithm execution in actual engineering, 0.5-1 is recommended in the invention, and the unit is m.
The invention also provides an initial trajectory generation system in the online sequence convex optimization of the aircraft, which comprises computer equipment; the computer device is configured or programmed for performing the steps of the above-described method.
To facilitate the acquisition of the relevant data, the computer device communicates with a navigation device of the aircraft.
Compared with the prior art, the invention has the beneficial effects that: the method can effectively solve the problem of low convergence speed of the on-line sequence convex optimization algorithm caused by large initial track error, effectively improves the precision of generating the initial track in a subsequent planning period (not including a first planning period), and reduces the iteration times of the sequence convex optimization algorithm, thereby improving the convergence speed, and ensuring the landing guidance precision.
Detailed Description
Aiming at the problem of guidance of a first-stage recovery landing segment of a carrier rocket, the method firstly generates an initial track of a first planning period based on the number of fixed discrete points; secondly, determining initial time and terminal time for performing online sequence convex optimization in the current planning cycle, and discretizing the time range; if the previous planning period can obtain an effective reference track, performing linear interpolation on the reference track; otherwise, carrying out linear interpolation by using the reference track of the last but one planning cycle so as to obtain the state quantity of each discrete point in the time range; and finally, forming an initial track for online sequential convex optimization in the current planning period based on the state quantities at the discrete points.
In the embodiment of the invention, the initial state of the landing segment is x by taking one-stage recovery of a certain type of carrier rocket as an example0＝3528.5m，y0＝-715.7m，z0＝0，Vx0＝-207.0m/s，Vy0＝87.7m/s，Vz0The mass was 23000kg at-0.1 m/s. The planning period is Tplanning＝2s，εH1 m. The sequence convex optimization algorithm can refer to: m Szmuk, B Acikmese, A W Berning. Successive conformation for fuel-optimal powered mapping with aerogenic drag and non-conditional constraints [ C].AIAA Guidance,Navigation,and Control Conference.San Diego,California USA,2016。
1) The number of discrete points adopted by the online sequence convex optimization method is set to be N, N is a positive integer, generally 10-100 can be taken, and the flight time range of the 1 st track planning is
Figure BDA0002801761990000051
Figure BDA0002801761990000052
The value of 0 is generally taken to be 0,
Figure BDA0002801761990000053
any real number between 20-60s may be taken. All the position speed state quantities are described in a landing coordinate system, and the terminal state of a landing segment is set to be Sf＝[0 0 0 0 0 0]ΤThe first three components represent the position in three directions and the last three components represent the velocity in three directions. After entering the landing segment, the initial state corresponding to the 1 st planning period measured by the navigation equipment is
Figure BDA0002801761990000054
Assuming a current state
Figure BDA0002801761990000055
To terminal state SfThe position velocity of (a) varies linearly with time, each uniformly discrete time in the time range being
Figure BDA0002801761990000056
The superscript 1 represents the 1 st planning cycle, the subscript represents the discrete time sequence number, and the initial trajectory of the 1 st planning cycle is
Figure BDA0002801761990000057
Corresponding to a time variation range of
Figure BDA0002801761990000058
Let the sequence number k of the planning period be 1, wherein
Figure BDA0002801761990000059
The values of the x-direction component of the position at different discrete times,
Figure BDA00028017619900000510
for the values of the y-direction component of the position at different discrete times,
Figure BDA00028017619900000511
the values of the z-direction component of the position at different discrete times,
Figure BDA00028017619900000512
the values of the velocity x-direction component at different discrete times,
Figure BDA00028017619900000513
for the values of the velocity y-direction component at different discrete times,
Figure BDA00028017619900000514
the value of the component in the z direction of the speed at different discrete moments is obtained, and the corresponding moment at each discrete point is
Figure BDA00028017619900000515
Wherein
Figure BDA00028017619900000516
2) Based on an initialization trajectory
Figure BDA0002801761990000061
Executing an online sequence convex optimization algorithm, and outputting a reference track R obtained in the kth planning cycle after the algorithm is converged(k)；
3) The navigation equipment measures to obtain the current motion state as
Figure BDA0002801761990000062
Representing the position and velocity components in three directions, respectively. Will be provided with
Figure BDA0002801761990000063
As an initial time of the (k + 1) th planning cycle, and
Figure BDA0002801761990000064
state of motion
Figure BDA0002801761990000065
As an initialization of the (k + 1) th planning cycleA state;
4) when in use
Figure BDA0002801761990000066
When the rocket is in the ground state, the rocket is explained to be in the ground state, and the program is ended; otherwise, turning to the step 5;
5) to be provided with
Figure BDA0002801761990000067
The time range of the online sequence projection is carried out for the (k + 1) th planning period, the interval is equally divided into N-1 intervals, the corresponding time of each discrete point in the time range is obtained and recorded as
Figure BDA0002801761990000068
And is
Figure BDA0002801761990000069
6) If the reference track R is obtained in the k-th track planning period(k)If the path is not empty, namely the path planning is successful, executing the step 7, otherwise, executing the step 8;
7) reference trajectory obtained based on kth planning cycle
Figure BDA00028017619900000610
Linear interpolation is carried out, including linear interpolation of six state quantities of position and speed, so as to obtain six state quantities at each discrete moment
Figure BDA00028017619900000611
The value of (A) is recorded as
Figure BDA00028017619900000612
And taking the initial trajectory as an initialization trajectory for performing online sequence convex processing on the k +1 th planning period. Changing k to k +1, and turning to the step 2;
8) reference track obtained based on k-1 planning cycle
Figure BDA00028017619900000613
Performing linear interpolation, including position velocityLinear interpolation of six state quantities in total, so as to obtain six state quantities at each discrete time
Figure BDA00028017619900000614
The value of (A) is recorded as
Figure BDA00028017619900000615
And taking the initial trajectory as an initial trajectory for performing online sequence convex processing on the k +1 th planning cycle. Changing k to k +1, and turning to the step 2;
the invention also provides an initial trajectory generation system in the online sequential convex optimization of the aircraft, which comprises computer equipment; the computer device is configured or programmed for performing the steps of the above-described embodiment method. To facilitate the acquisition of the relevant data, the computer device communicates with a navigation device of the aircraft. The navigation device is used for measuring the current motion state of the aircraft.
An experiment is given below to verify the beneficial effects of the present invention.
In order to verify that the method provided by the invention can improve the convergence rate of the sequence convex optimization algorithm, the following experiment compares the method of the invention with an initial trajectory generation method adopting linear hypothesis. Table 1 compares the results of the number of iterations required for the two methods applied in the sequence convex optimization algorithm. It can be seen that the method for generating the initial trajectory is beneficial to reducing the iteration times of the sequence convex optimization algorithm and improving the convergence rate. The landing guidance accuracy comparison under the two methods is shown in table 2, and it can be seen that the two methods can both meet the requirement of the landing guidance accuracy. The method can enable the sequence convex optimization algorithm to have higher convergence speed under the condition that the landing guidance accuracy is basically consistent.
TABLE 1 comparison of sequence convex iterations under different methods
Figure BDA0002801761990000071
Figure BDA0002801761990000081
Note that "X + 1" in table 1 above indicates that the linear hypothesis generation method is performed 1 time, and the sequence convex is iterated X times; "X" indicates that the method provided by the invention is adopted to generate an initial track, and the sequence is subjected to the convex iteration for X times.
TABLE 2 comparison of landing guidance accuracy under different methods
Linear hypothesis generation method Method of the invention
x 0.0340 0.0323
y -0.0625 0.0720
z 0.0118 0.0135
Vx 0.0058 0.0073
Vy -0.2070 -0.2392
Vz 0.0393 0.0450

Claims (8)

1. An initial trajectory generation method in online sequential convex optimization of an aircraft is characterized by comprising the following steps:
in a first planning period, generating an initial track by adopting a linear hypothesis method;
starting from the second planning period, determining the initial track used for online sequence convex optimization in the current period based on the reference track successfully planned last time.
2. The method for generating the initial trajectory in the aircraft online sequential convex optimization according to claim 1, wherein in the 1 st planning period, the specific implementation process for generating the initial trajectory by using the linear hypothesis method comprises: set from the current state
Figure FDA0002801761980000011
To terminal state SfIs linearly changed with time from the current state
Figure FDA0002801761980000012
To terminal state SfTime range of
Figure FDA0002801761980000013
Each uniformly discrete time is
Figure FDA0002801761980000014
The 1 st planning period is denoted by the superscript 1, and N is the number of discrete points, the initial trajectory of the current planning period is
Figure FDA0002801761980000015
Let the sequence number k of the planning period be 1, wherein
Figure FDA0002801761980000016
The values of the x-direction component of the position at different discrete times,
Figure FDA0002801761980000017
for the values of the y-direction component of the position at different discrete times,
Figure FDA0002801761980000018
the values of the z-direction component of the position at different discrete times,
Figure FDA0002801761980000019
the values of the velocity x-direction component at different discrete times,
Figure FDA00028017619800000110
for the values of the velocity y-direction component at different discrete times,
Figure FDA00028017619800000111
the subscripts of the position component and the velocity component represent the serial numbers of the discrete points,
Figure FDA00028017619800000112
current state
Figure FDA00028017619800000113
Terminal state Sf＝[0 0 0 0 0 0]Τ。
3. The method for generating an initial trajectory in an aircraft online sequential convex optimization according to claim 2,
Figure FDA00028017619800000114
the value of the oxygen is 0, and the oxygen concentration is less than or equal to zero,
Figure FDA00028017619800000115
the value range is 20-60 s.
4. The method for generating the initial trajectory in the online sequential convex optimization of the aircraft according to any one of claims 1 to 3, wherein starting from the second planning cycle, the initial trajectory used in the online sequential convex optimization in the current cycle is determined based on the reference trajectory successfully planned last time, and the implementation process includes: determining a time range for performing online sequence convex optimization in the current planning period, wherein the time range comprises initial time and terminal time, and discretizing the time range; if the previous planning period obtains an effective reference track, performing linear interpolation on the reference track; otherwise, carrying out linear interpolation by using the reference track of the last but one planning cycle so as to obtain the state quantity of each discrete point in the time range; and the state quantities at the discrete points form an initial track for performing online sequential convex optimization in the current planning period.
5. The method for generating the initial trajectory in the online sequential convex optimization of the aircraft according to claim 4, wherein the specific implementation process for acquiring the state quantity at the discrete point comprises:
1) based on an initialization trajectory
Figure FDA0002801761980000021
Executing an online sequence convex optimization algorithm, and outputting a reference track R obtained in the kth planning cycle after the algorithm is converged(k)；
2) The current motion state is obtained by measurement
Figure FDA0002801761980000022
Will be provided with
Figure FDA0002801761980000023
As an initial time of the (k + 1) th planning cycle, and
Figure FDA0002801761980000024
Tplanningindicating planning cycle, motion state
Figure FDA0002801761980000025
As the initial state of the (k + 1) th planning cycle;
3) when in use
Figure FDA0002801761980000026
When so, ending; otherwise, turning to the step 4); wherein epsilonHJudging the tolerance for the landing condition;
4) to be provided with
Figure FDA0002801761980000027
The time range of online sequence convex optimization is carried out for the (k + 1) th planning cycle, the time range is equally divided into N-1 intervals, and the corresponding time of each discrete point in the time range is obtained and recorded as
Figure FDA0002801761980000028
And is
Figure FDA0002801761980000029
5) If the reference track R is obtained in the k-th track planning period(k)If the path is not empty, namely the path planning is successful, executing step 6); otherwise, turning to step 7);
6) reference trajectory obtained based on kth planning cycle
Figure FDA00028017619800000210
Linear interpolation is performed to obtain a reference trajectory R(k)At each discrete time
Figure FDA00028017619800000211
Is taken as
Figure FDA0002801761980000031
Will be provided with
Figure FDA0002801761980000032
Taking the k +1 th planning period as an initialization track for online sequential convex optimization, adding 1 to the value of k, and turning to the step 1);
7) reference track obtained based on k-1 planning cycle
Figure FDA0002801761980000033
Performing linear interpolation to obtain R(k-1)At each discrete time
Figure FDA0002801761980000034
Is taken as
Figure FDA0002801761980000035
Will be provided with
Figure FDA0002801761980000036
And (4) taking the initial trajectory as the k +1 th planning period for online sequence convex, adding 1 to the value of k, and turning to the step 1).
6. The method for generating initial trajectory in aircraft online sequential convex optimization according to claim 5, wherein εHTaking 0.5-1, and taking the unit as m.
7. An initial trajectory generation system in an aircraft online sequential convex optimization is characterized by comprising computer equipment; the computer device is configured or programmed for carrying out the steps of the method according to one of claims 1 to 6.
8. The system of claim 7, wherein the computer device is in communication with a navigation device of the aircraft.
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