CN112693631B - Initial trajectory generation method and system in online sequential convex optimization of aircraft - Google Patents
Initial trajectory generation method and system in online sequential convex optimization of aircraft Download PDFInfo
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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
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 is controlled by a variable thrust engine 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 using a linear hypothesis method includes:
set from the current state
To terminal state S f Is linearly changed with time from the current state
To terminal state S f Time range of
Each uniformly discrete time is
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
Let the sequence number k of the planning period be 1, wherein
The values of the x-direction component of the position at different discrete times,
for the values of the y-direction component of the position at different discrete times,
the values of the z-direction component of the position at different discrete times,
the values of the velocity x-direction component at different discrete times,
for the values of the velocity y-direction component at different discrete times,
the subscripts of the position component and the velocity component represent the serial numbers of the discrete points,
current state
Terminal state S f ＝[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.
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 initialized trajectories
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
Will be provided with
As an initial time of the (k + 1) th planning cycle, and
T planning indicating planning cycle, motion state
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
When so, ending; otherwise, turning to the step 4); wherein epsilon H Judging 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
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
And is provided with
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 
Linear interpolation is performed to obtain a reference trajectory R (k) At each discrete time
Is taken as
Will be provided with
As the (k + 1) th planPeriodically carrying out an initialization track of online sequence convex, 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
Performing linear interpolation to obtain R (k-1) At each discrete time
Is taken as
Will be provided with
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).
ε H The 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 following beneficial effects: 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 the initial time and the terminal time of the online sequential convex optimization of 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 example 0 ＝3528.5m，y 0 ＝-715.7m，z 0 ＝0，V x0 ＝-207.0m/s，V y0 ＝87.7m/s，V z0 The mass was 23000kg at-0.1 m/s. The planning period is T planning ＝2s，ε H 1 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
The value of 0 is generally taken to be 0,
any real number between 20-60s may be taken. All position speed state quantities areDescribing in a land coordinate system, the terminal state of the landing segment is set to S f ＝[0 0 0 0 0 0] Τ The 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
Assuming a current state
To terminal state S f The position velocity of (a) varies linearly with time, each uniformly discrete time in the time range being
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 
Corresponding to a time variation range of
Let the planning period number k equal to 1, wherein
The values of the x-direction component of the position at different discrete times,
the values of the y-direction component of the position at different discrete instants,
the values of the z-direction component of the position at different discrete times,
the values of the velocity x-direction component at different discrete times,
for the values of the velocity y-direction component at different discrete times,
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
Wherein
2) Based on an initialization trajectory
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
Representing the position and velocity components in three directions, respectively. Will be provided with
As an initial time of the (k + 1) th planning cycle, and
state of motion
As the initial state of the (k + 1) th planning cycle;
4) when in use
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
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 
And is
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
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
The value of (A) is recorded as
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
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
The value of (A) is recorded as
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
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 (6)
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 an initial track used for online sequence convex optimization in the current period based on the reference track successfully planned last time; the implementation process comprises the following steps: 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; the state quantities at the discrete points form an initial track for performing online sequential convex optimization in the current planning period;
the specific implementation process of acquiring the state quantity at the discrete point comprises the following steps:
1) based on an initialization trajectory
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 
Will be provided with
As an initial time of the (k + 1) th planning cycle, and
T planning indicating planning cycle, motion state
As the initial state of the (k + 1) th planning cycle;
3) when in use
When so, ending; otherwise, turning to the step 4); wherein epsilon H Judging the tolerance for the landing condition;
4) to be provided with
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
And is
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
Linear interpolation is performed to obtain a reference trajectory R (k) At each discrete time
Is taken as
Will be provided with
As the (k + 1) th planning cycleThe line online sequence convex optimization initialization track is carried out, the value of k is added with 1, and the step 1) is carried out;
7) reference track obtained based on k-1 planning cycle
Performing linear interpolation to obtain R (k-1) At each discrete time
Is taken as
Will be provided with
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).
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
To terminal state S f Is linearly changed with time from the current state
To terminal state S f Time range of
Each uniformly discrete time is
The 1 st programming cycle is indicated by the superscript 1, N is the number of discrete pointsTo that end, the initial trajectory of the current planning cycle is
Let the sequence number k of the planning period be 1, wherein
The values of the x-direction position component at different discrete times,
for the values of the y-direction position component at different discrete times,
for the values of the z-direction position component at different discrete times,
the values of the x-direction velocity component at different discrete times,
for the values of the y-direction velocity component at different discrete times,
the subscripts of the position component and the velocity component represent the serial numbers of discrete points,
current state
Terminal state
S f ＝[0 0 0 0 0 0] T 。
3. The aircraft online sequence of claim 2An initial trajectory generation method in convex optimization, characterized in that, 
The value of the oxygen is 0, and the oxygen concentration is less than or equal to zero,
the value range is 20-60 s.
4. The method for generating initial trajectory in aircraft online sequential convex optimization according to claim 1, wherein ε H Taking 0.5-1, and taking the unit as m.
5. 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 4.
6. The system of claim 5, wherein the computer device is in communication with a navigation device of the aircraft.
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