CN115291504B - Rocket sub-level recovery landing zone power descent guidance method based on tail end error - Google Patents

Rocket sub-level recovery landing zone power descent guidance method based on tail end error Download PDF

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CN115291504B
CN115291504B CN202210601592.7A CN202210601592A CN115291504B CN 115291504 B CN115291504 B CN 115291504B CN 202210601592 A CN202210601592 A CN 202210601592A CN 115291504 B CN115291504 B CN 115291504B
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CN115291504A (en
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杨广文
陈宇澍
陈海鹏
王禄
甘庆忠
张武生
柳嘉
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National Supercomputing Center In Wuxi
Shanghai Aerospace Control Technology Institute
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Shanghai Aerospace Control Technology Institute
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Abstract

The invention provides a rocket sub-stage recovery landing zone power descent guidance method based on terminal errors, relates to a rocket guidance recovery method, and solves the problem of rocket sub-stage vertical recovery landing zone power descent guidance under nonlinear aerodynamic force by converting a PDG problem under nonlinear aerodynamic force into SOCP problem solving. The method has the advantages of low calculation cost, less calculation resource occupation, effective suppression of position errors in specific directions, feasibility of sub-problems under reasonable assumption, and interpretation; meanwhile, programs running on domestic equipment such as a processor on a rocket and the like are all independently researched and developed, and only calculation results of open source software are needed when general equipment is preprocessed.

Description

Rocket sub-level recovery landing zone power descent guidance method based on tail end error
Technical Field
The invention relates to a rocket guidance recovery method, in particular to a rocket sub-level recovery landing zone power descent guidance method based on terminal errors.
Background
The vertical recovery landing stage of the rocket stage needs to start the engine to perform reverse thrust deceleration, and the process is called power descent. In order to realize accurate vertical soft landing, power Descent Guidance (PDG) is needed, namely track planning is carried out according to the current state observed by the sensor and the preset drop point position, and a control signal is generated.
Because the initial conditions (speed and position) of the starting moment of the mission (engine ignition) are large in dispersion deviation, the track is difficult to calculate in advance, and the power reduction guidance needs to be carried out on line so as to meet the process constraints such as thrust adjustment and residual fuel and the terminal constraints such as position, speed and gesture, and therefore the established flight mission is realized. Therefore, the power reduction guidance has high real-time requirements. However, the arrow-mounted computer is often relatively insufficient in computing power due to the considerations of volume, weight, power consumption, radiation protection and the like, and the contradiction in computing speed is very prominent. Particularly, the influence of nonlinear aerodynamic force must be considered in the recovery of rocket launching sub-stages in the earth atmosphere, so that the calculation amount is further greatly increased, and the challenges in real-time performance are more serious. In addition, the power reduction guidance also faces the technical difficulties of high requirements on landing position, speed and attitude precision, minimized fuel consumption and the like.
For PDG problem solving without considering aerodynamic force, some more mature research results are internationally available, and representative are a series of papers published by JPL laboratories and university of Washington, cooperation, etc. In the work, the PDG problem is systematically and formally described, the motion equation and various constraints of the spacecraft are analyzed, and solutions such as lossless bulge and quality approximation bulge are provided for non-bulge constraint in the problem, and finally the solution is converted into a second-order cone normalization (SOCP) problem to be solved. If the total flight time is fixed, the PDG problem without taking aerodynamic force into consideration can be converted into a single SOCP problem to be solved, but the total flight time needs to be searched through multiple attempts (such as a dichotomy method, interpolation and the like). If the total flight time is adjusted, the problem of non-pneumatic PDG is similar to the problem of pneumatic PDG, and the problem is solved by converting the sequence of convex transformation into a series of SOCP problems.
While the PDG solution considering nonlinear aerodynamic force is still in the research stage of published results. The washington university adopts a sequential salifying method (hereinafter referred to as an acceleration error method) for relaxing based on acceleration errors to solve the PDG problem considering nonlinear aerodynamic forces, solves the total flight time through local approximate salifying, and introduces acceleration errors to avoid the problem. The algorithm has practical application prospect, but the calculated amount is greatly increased compared with that of the calculation without aerodynamic force, and the requirement on the performance of an arrow-borne computer is very high. In addition, the acceleration error represents the degree of violation of the dynamic constraint based on the physical law, and when any constraint such as the end position, the speed, the attitude constraint and the like cannot be satisfied, the discomfort of the problem is reflected on the acceleration error, and only a solution with a large acceleration error is obtained, but such a solution is not present in practice and cannot reflect the practically reachable flight trajectory and the end state. SpaceX is not disclosed, is expected to be closely related to the work of the university of JPL and washington, and requires high performance arrow-borne computers. Beihang University solves the PDG problem under the two-dimensional condition considering the action of air resistance and lifting force, and proposes an algorithm which does not need to solve the total flight time, but still needs to solve the problem through sequential salinization, and the SOCP problem obtained through local linearization may not be feasible, thereby causing solving failure.
The SOCP problem is typically solved by a dedicated solver. The JPL series paper uses a SOCP problem efficient solver BSOCP (the program is not disclosed, but an algorithm scheme is disclosed in the paper) which is developed by the JPL series paper, under the condition of no pneumatic operation, the calculation efficiency is very high due to the good sparsity of the problem structure, but under the condition of pneumatic operation, the sparsity of the problem structure is slightly poor, the number of non-zero elements of a coefficient matrix can be greatly increased when the algorithm is used for solving a linear equation set, and the calculation efficiency is greatly reduced. In the currently disclosed solver, for the common configuration of the PDG problem, the efficiency of the ECOS is highest, is substantially lower than BSOCP when there is no pneumatic operation, and is expected to be higher than BSOCP when there is pneumatic operation, but the computational efficiency still has room for improvement, and the hot start is not supported, so that the solution acceleration convergence of the early-stage sub-problem in the sequence salinization is not facilitated.
At present, the main difficulties of solving the power drop guidance problem under the nonlinear aerodynamic force effect on line are as follows:
Firstly, constraint needs to be effectively relaxed, so that the SOCP sub-problem of local approximation is feasible under reasonable assumption, and solving failure caused by infeasibility of factor problems is avoided. Secondly, the problem relaxation and the excessively strong nonlinearity introduced in the discrete process are avoided, so that slow convergence is caused, and the number of sub-problems to be solved is increased. Thirdly, the structure for avoiding the sub-problems is too complex, so that the calculation cost of the single sub-problem is excessively increased. And fourthly, efficiently solving SOCP problems.
Disclosure of Invention
Aiming at the technical problems, the invention provides a tail-end error-based rocket sublevel recovery landing zone power descent guidance method, which aims to solve the problem of rocket sublevel vertical recovery landing zone power descent guidance under nonlinear aerodynamic force.
In order to achieve the above purpose, the technical scheme adopted by the invention is as follows:
The invention provides a rocket sub-level recovery landing zone power descent guidance method based on terminal errors, which comprises the following steps of
Step 101: inputting initial total flight time t f, discrete time step number k f, sub-problem number upper limit n SC, time step change trust zone upper limit eta Δt, thrust change trust zone upper limit eta T and trust zone adjustment coefficient beta;
Step 102: initializing;
Step 103: if i=1, then SOCP problem constraints are generated, in which case either no trust zone constraints are used, or a larger trust zone boundary is used; if i > 1, updating SOCP the problem constraint;
Step 104: solving SOCP problems; calculating the position and speed error of the tail end through fine grid numerical simulation;
Step 105: calculating an improvement ratio ζ= (J L0,i-JL0,i-1)/(JL1,i-JL1,i-1); if ζ is greater than or equal to ζ max, if a trusted region boundary is activated, multiplying β by the activated boundary corresponding to the trusted region radius (η Δt or η T); if ζ is less than or equal to ζ min, dividing the radius of the trust zone η Δt,ηT by β; if ζ.ltoreq.0, rejecting SOCP the problem, resetting to the solution of the last sub-problem, i.e. m i[k]＝mi-1[k],Γi[k]＝Γi-1 [ k ],
ri[k]＝ri-1[k],vi[k]＝vi-1[k],ai[k]＝ai-1[k],aR,i[k]＝aR,i-1[k],k∈{0,1,…,kf},Δti＝Δti-1;
Step 106: updating the total flight time t f;
step 107: if the end position and speed error is smaller than the preset limit, step 109 is executed;
Step 108: if i is less than n SC, i=i+1, repeating steps 103 to 106; if i=n SC, then step 109 is performed;
step 109: outputting total flight time T f, mass m, position r, speed v and thrust T;
Wherein, Is the objective function value of the plan, J L1＝-m(kf)+ωκr||r[kf]||+ωκv||v[kf || is the objective function value of the simulation; m, r, v are the mass, position, velocity in SOCP solution,/>The quality, position and speed calculated through numerical simulation are calculated, i is the serial number of the sub-problem;
The initialization in step 102 is specifically:
According to the rocket sub-level recovery landing zone power descent guidance method based on the tail end error, preferably, hot start can be supported, and acceleration is carried out by utilizing the correlation among SOCP problems; when the hot start is used, the method also comprises the step of outputting the initial value of the current SOCP problem (x 0,y0,s0) through a SOCP problem hot start initial value correction method before the 'solution SOCP problem';
The 'SOCP problem hot start initial value correction method' comprises the following steps:
step 201: solution of input existing early SOCP sub-problem The current sub-problem equation constrains the coefficient matrix A, the right-hand term b, the cone constraint dimension (l, S 1,S2,…,Sm), the correction coefficient η 0 (default value 0.001);
Step 202: initializing, η=max (1/(|a| ∞+||b||∞),η0);
step 203: initializing, i=1;
Step 204: i+＝Sj，/>
Step 205, if i is less than or equal to m, repeating step 204; if i > m, go to step 206;
Step 206: the initial value of the current SOCP question is output (x 0,y0,s0).
The rocket stage recovery landing zone power descent guidance method based on the tail end error provided by the invention preferably further comprises outputting an initial value (x 0,y0,s0) of the current SOCP problem by a SOCP problem hot start initial value correction method before solving the SOCP problem; step 105 may be omitted.
The technical scheme has the following advantages or beneficial effects:
According to the rocket sub-stage recovery landing zone power descent guidance method based on the tail end error, which is provided by the invention, the PDG problem under nonlinear aerodynamic force is converted into SOCP problem to be solved, so that the rocket sub-stage vertical recovery landing zone power descent guidance problem under nonlinear aerodynamic force is solved. The method can realize low calculation cost, occupies less calculation resources, can effectively suppress position errors in specific directions, can enable sub-problems to be feasible under reasonable assumption, and has interpretation; meanwhile, programs running on domestic equipment such as a processor on a rocket and the like are fully independently researched and developed, and only calculation results of open source software are needed when general equipment is preprocessed.
Detailed Description
The invention will be further illustrated with reference to specific examples, which are not intended to be limiting.
Example 1:
The PDG original problem of nonlinear aerodynamic force is considered, namely, under a specific initial value (including initial position, speed and fuel quality of the rocket, taking a preset landing point as an origin of a coordinate system), track planning is carried out by adjusting the magnitude and the direction of thrust, so that the rocket can accurately land on the preset landing point, the direction is vertical to the ground upwards during landing, the speed is zero, and the fuel consumption is minimized. In the aspect of rocket attitude, namely, the rocket tail is approximately considered to point to the thrust direction, and the influence of sideslip angle is not considered.
The problem can be described as
Objective function:
Initial and edge values:
Power constraint:
state constraint:
control constraints:
Wherein r is position, v is speed, a is acceleration, T is thrust, and m is mass; θ gs is the minimum included angle (anti-collision) between the connecting line of the current position of the rocket and the landing point and the ground, and θ T,max is the maximum included angle between the thrust direction and the speed direction; when no special description is given, the terms "x" and "x" are both the two norms of the vector x. t f is the total time of flight, For the lower and upper limits of the thrust rate of change, ρ 0 is the atmospheric density at the predetermined drop point, C ρ is the atmospheric density attenuation coefficient, m dry is the mass of the rocket body structure (without fuel), α is the ratio of the fuel consumption rate to the thrust, C D is the air resistance coefficient, and S ref is the rocket reference area.
According to the thought of literature, the control constraint is subjected to lossless convexity, and is converted into
||T(t)||≤Γ(t)
0≤Tmin≤Γ(t)≤Tmax
The original problem is now transformed into a series of partial linear approximation sub-problems for solving. To effectively control the computation and make the local approximation sub-problem generally viable, the present invention introduces a relaxation scheme based on end-point errors. The proposal relaxes the end position and speed constraint, namely, allows the end position and speed to have any error, and adds the upper bound of the position and speed error into the objective function for punishment.
The discretized PDG local linear approximation sub-problem (numbered i) can be described as:
objective function:
Initial and edge values:
Power constraint:
wherein, dk is not used as solving variable, substituting into a k when actually solving;
state constraint:
control constraints:
end error constraint:
trust zone constraints:
Where D is air resistance, Δt is discrete time step, κ r,κv is penalty factor, and should take a larger value to suppress end position and velocity error, η Δt,ηT is the upper bound of the confidence domain for time step and thrust variation between adjacent sub-problems.
When the ith sub-problem (hereinafter referred to as sub-problem i) is solved, the previous i-1 sub-problem is solved, and the variable value is determined. Therefore, nonlinearity does not exist in the power constraint in the discrete PDG local linear approximation sub-problem solution, and the nonlinearity cannot be caused; while the other constraints are convex. Thus for each sequence number i, the partial linear approximation, discretized PDG partial linear approximation sub-problem is a convex optimization problem. More specifically, the discretized PDG local linear approximation sub-problem is a second order cone optimization problem (SOCP), i.e., the PDG problem under nonlinear aerodynamic forces can be converted to SOCP problem solution.
The standard form of SOCP problem is:
Wherein, Representing a linear cone, l being the dimension of the linear cone; k S represents a second order cone, and m is the number of second order cones;
Linear cone And second order cone K S are defined as: /(I)
In this embodiment, the discretized PDG local linear approximation sub-problem can be converted into SOCP problem standard form by:
The unconstrained omega conversion form is as follows: ω=ω +-ω-, wherein
The linear constraint h T ω < d translates to: h T(ω+-ω-)+ωs = d, wherein ω +,ω-,ωs∈KL;
The secondary constraint ω < d is translated into:
Thus, in this embodiment, the PDG problem under nonlinear aerodynamic forces can be solved by converting the sequence convex into a series of local linear approximation sub-problems. The invention provides a rocket sublevel recovery landing zone power descent guidance method based on terminal error (hereinafter referred to as terminal error method) provided in embodiment 1 of the invention, which comprises the following steps:
Step 101: inputting initial total flight time t f, discrete time step number k f, sub-problem number upper limit n SC, time step change trust zone upper limit eta Δt, thrust change trust zone upper limit eta T and trust zone adjustment coefficient beta;
Step 102: initializing;
Step 103: if i=1, then SOCP problem constraints are generated, in which case either no trust zone constraints are used, or a larger trust zone boundary is used; if i > 1, updating SOCP the problem constraint;
Step 104: solving SOCP problems; calculating the position and speed error of the tail end through fine grid numerical simulation;
Step 105: calculating an improvement ratio ζ= (J L0,i-JL0,i-1)/(JL1,i-JL1,i-1); if ζ is greater than or equal to ζ max, if a trusted region boundary is activated, multiplying β by the activated boundary corresponding to the trusted region radius (η Δt or η T); if ζ is less than or equal to ζ min, dividing the radius of the trust zone η Δt,ηT by β; if ζ.ltoreq.0, rejecting SOCP the problem, resetting to the solution of the last sub-problem, i.e. m i[k]＝mi-1[k],Γi[k]＝Γi-1 [ k ],
ri[k]＝ri-1[k],vi[k]＝vi-1[k],ai[k]＝ai-1[k],aR,i[k]＝aR,i-1[k],k∈{0,1,…,kf},Δti＝Δti-1;
Step 106: updating the total flight time t f;
step 107: if the end position and speed error is smaller than the preset limit, step 109 is executed;
Step 108: if i is less than n SC, i=i+1, repeating steps 103 to 106; if i=n SC, then step 109 is performed;
step 109: outputting total flight time T f, mass m, position r, speed v and thrust T;
Wherein, Is the objective function value of the plan, J L1＝-m(kf)+ωκr||r[kf]||+ωκv||v[kf || is the objective function value of the simulation; m, r, v are the mass, position, velocity in SOCP solution,/>The quality, position and speed calculated through numerical simulation are calculated, i is the serial number of the sub-problem;
step 102 is initialized specifically as follows:
To further increase computational efficiency, a warm start may be employed for SOCP problem solving. The hot start refers to that when a plurality of convex optimization sub-problems need to be solved such as sequence salification and the like and the current sub-problem has small parameter change relative to a certain solved sub-problem, an initial value is generated through solution calculation of a previous sub-problem, so that an initial value error is reduced and the solution is accelerated. The interior point method adds a penalty through the barrier function, limiting the search area to the interior of the constraint space. The gradient, curvature, and rapid change of the barrier function near the constraint boundary tend to make hot start of the interior point method relatively difficult. If the previous solution is already close to the constraint boundary, taking it as an initial value, the update direction is often poor in effectiveness, the allowable step size is small, and the subsequent iteration step converges slowly. To avoid the above problems, the initial value needs to be adjusted to deviate from the boundary. The specific adjustment mode is to add an offset constructed based on a cold start initial value to a term approaching a constraint boundary in the existing solution.
Solving SOCP problems using the interior point method generally requires consideration of not only the original problem but also the dual problem. The dual problem form of SOCP standard problems is:
in contrast, in the hot start, it is necessary to deviate the binary variable s satisfying the same cone constraint from the boundary as well as the original variable x from the boundary. Thus, in this embodiment, outputting the initial value of the current SOCP problem (x 0,y0,s0) by the SOCP problem hot start initial value correction method is also included before "solving SOCP problem";
the SOCP problem hot start initial value correction method specifically comprises the following steps:
step 201: solution of input existing early SOCP sub-problem The current sub-problem equation constrains the coefficient matrix A, the right-hand term b, the cone constraint dimension (l, S 1,S2,…,Sm), the correction coefficient η 0 (default value 0.001);
Step 202: initializing, η=max (1/(|a| ∞+||b||∞),η0);
step 203: initializing, i=1;
Step 204:
Step 205, if i is less than or equal to m, repeating step 204; if i > m, go to step 206;
Step 206: the initial value of the current SOCP question is output (x 0,y0,s0).
If the number of steps in a single SOCP problem solution is small, there may not be near optimal solutions, but only some improvement, so the trust domain cannot be scaled according to the objective function improvement, and should be kept constant. At this point, step 105 may be omitted; the omitted rocket sub-level recovery landing section power descent guidance method based on the tail end error specifically comprises the following steps:
step 301: inputting initial total flight time t f, discrete time step number k f, sub-problem number upper limit n SC, time step change trust zone upper limit eta Δt, thrust change trust zone upper limit eta T and trust zone adjustment coefficient beta;
Step 302: an initialization is performed such that the data of the data storage device,
Step 303: if i=1, then SOCP problem constraints are generated, in which case either no trust zone constraints are used, or a larger trust zone boundary is used; if i > 1, updating SOCP the problem constraint;
step 304: outputting an initial value (x 0,y0,s0) of the current SOCP problem by a SOCP problem hot start initial value correction method;
step 305: solving SOCP problems; calculating the position and speed error of the tail end through fine grid numerical simulation;
Step 306: updating the total flight time t f;
step 307: if the end position and speed error is smaller than the preset limit, go to step 309;
Step 308: if i < n SC, i=i+1, repeating steps 303 to 306; if i=n SC, then step 309 is performed;
Step 309: the total flight time T f, the mass m, the position r, the speed v and the thrust T are output.
The embodiment 1 of the invention has the following beneficial effects:
1. The calculation cost is low. The improvement of the calculation amount comes mainly from three aspects: and one is a single SOCP problem solving calculation. For single SOCP problem solving, compared with direct discretization solving of an original problem which is not loosened, when the end error method is converted into SOCP standard problem, the variable which represents the end speed mode exists, and only the end position mode needs to be added. The mode need only be implemented with a four-dimensional second order cone constraint. The variable and the increment of the calculated amount are less. And each time grid point of the acceleration error method needs to be added with a three-dimensional acceleration error, and N k four-dimensional second-order cone constraints or a 3N k +1-dimensional second-order cone constraint are needed. The traditional SOCP solver (based on [12] and similar algorithms), when solving a linear equation set in a single iteration step, the number of nonzero elements of a coefficient matrix caused by one second-order cone constraint is proportional to the square of the dimension, so that the calculated amount is lower by using N k four-dimensional second-order cone constraints, but the acceleration error is reasonably distributed to each time grid point by using high-dimensional second-order cone constraints, and huge calculated amount is increased by adopting any mode. The ECOS and FSOCP solvers carry out sparsification processing on the second-order cone constraint, the number of non-zero elements of the coefficient matrix caused by the second-order cone constraint is proportional to the order, the calculation speed of processing Gao Weier order cones is obviously higher than that of the traditional solver, but even if the solvers are used, the calculated quantity increment of an acceleration error method relative to an end error method is larger. And secondly, solving the number of SOCP problems. The number of SOCP problems to be solved is difficult to analyze theoretically, but the problem solved by the acceleration error method is more complex and has strong nonlinearity; and the method reduces the end error by minimizing the acceleration error in the objective function, and although the end error is 0 (ignoring the numerical discrete error) when the acceleration error is 0, the acceleration error and the end error have no direct corresponding relation when the acceleration error is not 0, which may lead to slower end error drop. And the end error method directly adds the end error into the objective function to minimize, so that the end error can be quickly reduced. Numerical experiments show that when cold start is adopted, the number of SOCP problems to be solved by the end error method is obviously lower than that of the end error method. 3. Is a hot start. By hot start, the initial error of SOCP problem can be reduced, thereby speeding up the solution. With the change of the solution in SOCP solving, the constraint is changed in practice, while the constraint is required to be unchanged in the single SOCP solving in sequence salinization, and the improvement brought to the original problem is limited when the solving precision is high. Through hot start, the upper bound of the number of solution steps of the single SOCP problem can be defined, namely, the problem SOCP is not solved each time, and the constraint is updated in time, so that the total calculation cost is reduced.
2. Sub-problems can be made feasible under reasonable assumptions and solutions are interpretable. The acceleration error method allows Xu Dongli constraint to have any error, namely allows the rocket to constraint any motion regardless of power, so long as other constraint does not conflict with each other, the SOCP sub-problem is certain to be feasible, but the existence of the acceleration error actually violates the physical rule, the obtained solution has no practical meaning when the acceleration error is non-zero (actually can not be reduced to a very low level), and the practical motion condition and the reachable end state can not be reflected. The end error method does not destroy the power constraint, and the control constraint (thrust magnitude, angle, rate of change) can be directly satisfied by setting, so its sub-problem feasibility depends on whether or not a feasible solution exists for the state constraint (including anti-collision, maximum speed and fuel quality). The fuel quality constraint, i.e., the fuel quality is non-negative, can be met by reasonably setting the total flight time (not greater than the time to consume all fuel with minimal thrust). When the maximum speed constraint meets the requirement at the initial speed, if the maximum pushing force is larger than the gravity (generally, the maximum pushing force is met), and when the speed approaches the maximum speed, the included angle between the combined force of the pushing force, the resistance and the gravity and the speed is larger than pi/2, so that the speed is not increased, and therefore, the method is feasible under the general condition. The collision constraint is || [ r x(t),rz(t)]T||tanθgs≤ry (t), i.e. is possible with a high initial value and a small downward velocity component, and extreme cases may not be possible. In general, the end error method allows the position and the speed of the rocket at the final time point to be any value allowed by other constraints, eliminates the infeasibility caused by the fact that the constraints of the end position and the speed cannot be met, and can enable the local approximate SOCP sub-problem to be feasible under the general reasonable condition. After the hot start is introduced, the single SOCP problem only solves a certain step number, even if the sub-problem is not feasible (the power constraint error cannot be reduced to be close to 0), the power constraint error can be reduced to a certain extent, the power constraint can be adjusted after the hot start, and the error of the approximate resistance is reduced, so that the infeasibility caused by the overlarge resistance initial value error is reduced. When the numerical discrete error and the local linear approximation error are not considered, the track planned by the end error method is the actual motion track, can reflect the actual intermediate state and the end state, and has sufficient interpretability.
3. Position errors in specific directions can be effectively suppressed. If a rocket lands, the safety is affected by the position error in the vertical direction, and the landing site in the horizontal direction is always in a certain range, so that the influence of the smaller position error is small. If all direction errors are required to be small, the time grid is required to be thinned, the iteration step number is increased, and the calculation cost is high. By applying the end error method, the direction error can be suppressed by only adding a larger weight to a specific direction when calculating the end position error, and reasonable errors are allowed to exist in other directions.
4. And the autonomous controllability is strong. By using a self-developed FSOCP solver (preprocessing in ground general equipment to generate operand address files for different discrete time steps), all libraries (except the C language standard library) running on domestic embedded equipment can be independently developed.
The guidance problem is solved by adopting the rocket sub-level recovery landing zone power descent guidance method based on the tail end error provided by the embodiment, and specific flight task parameters are set as shown in the following table 1:
TABLE 1 flight mission parameters
Note that: air density is calculated as ρ=ρ 0exp(-cρry). The density change coefficient c ρ is not accurate, and is currently approximately 0.0001, namely, the air density is reduced to 90.48% of the original air density every 1000m of the height.
The aerodynamic coefficients are as follows:
Mach number 0.2 0.3 0.5 1.0
Coefficient of resistance C a 0.32 0.32 0.51 0.53
Table 2 aerodynamic coefficients
The computing environment is a notebook computer, the CPU is R7 5800H (the basic frequency is 3.2GHz, the maximum acceleration frequency is 4.4 GHz), the memory is 16GB, and the program runs in series. Since the preprocessing can be done in advance, rather than acquiring the initial conditions to start, the calculation times FSOCP and ECOS only count the solving time, and do not count the preparation time. When the sequence is raised, the end condition is that the end position and the speed error are respectively less than 1m and 0.1m/s. The number of discrete time periods is fixed to 30 (corresponding number of time grid points is 31). The maximum solving sub-problem number is 30, and if the sub-problem number reaches the upper limit and still fails to meet the convergence condition, the solution fails.
Using the different total time of flight initial values, the number of sub-problems solved when each method reached the convergence condition, the calculated time and the remaining fuel pair ratios are shown in Table 3. During cold start, the ECOS automatically sets the number of iteration steps to be solved by single SOCP, and the upper limit of FSOCP iteration is 40 steps (if the iteration steps meet the convergence condition before reaching the upper limit, the iteration steps are terminated, otherwise, the iteration steps are terminated when reaching the upper limit). Comparing the results of the acceleration error method and the end error method, the end error method greatly reduces the number of SOCP sub-problems to be solved in cold start, and the average number of the sub-problems in the numerical result is only 60% of the number of the sub-problems in the latter. FSOCP is computationally efficient over ECOS. Thanks to the reduction of the number of sub-problems and the improvement of the efficiency of solving the single sub-problem, the average solving time of the end error method (FSOCP) is only 13.2% of that of the acceleration error method (ECOS). When FSOCP was used, the average calculation time of the end error method was 54.6% of the acceleration error method. Compared with cold start, hot start (only FSOCP supports) further greatly reduces the total calculation cost, although the number of sub problems is increased due to the small number of iterative steps of a single sub problem, the total iterative steps are greatly reduced, the calculation efficiency is improved by more than 5 times, and the average calculation time is only 2.1% of the acceleration error method (ECOS) and 8.8% of the acceleration error method (FSOCP). In terms of residual fuel quality, the PDG problem under nonlinear aerodynamic forces is a non-convex problem, and each method may converge to a different locally optimal solution, based on the results in table 3, the residual fuel of the end error method (FSOCP, hot start) is significantly better than the other methods, and the end error method (FSOCP, cold start) is slightly less than the acceleration error method (ECOS), but differs less.
TABLE 3 number of sub-problems solved when each method converged, calculation time and residual fuel comparison
To verify the ability of the end error method to suppress position errors in a specific direction, the components in the vertical direction in the end position errors were weighted according to different weights, and the obtained planning results are shown in table 4. In the solving process, an end error method (FSOCP, hot start, upper limit of iteration steps of each SOCP sub-problem is 5. It can be seen that by giving a larger weight to the vertical direction in the position error, the position error in the vertical direction can be effectively suppressed without increasing the number of time grids and greatly increasing the total iteration steps.
TABLE 4 planning results in which the vertical components in the terminal position errors are weighted by different weights
In order to compare the solving success rate and the calculating efficiency of the tail end error method and the acceleration error method, monte Carlo simulation is carried out. And adding normal random disturbance to the initial position, the speed and the mass by taking the original initial position, the original speed and the original mass as expectations, wherein the disturbance standard deviation of the position in each direction is 300m, the disturbance standard deviation of the speed in each direction is 30m/s, and the disturbance standard deviation of the fuel mass is 300kg. Taking various delays in actual conditions into consideration, and taking the position, speed and quality after 2.2s of numerical simulation as the initial value of planning. Each algorithm uses FSOCP solvers. The number of sub-problems at cold start is 30; when the upper limit of the iteration steps of the sub-problems is 1 and 5 respectively in hot start, the upper limit of the number of the sub-problems is 120 and 60. Terminating when the termination conditions (the end position and the speed error are respectively smaller than 1m and 0.1 m/s) are reached, and recording that the planning is successful; and when the upper limit of the number of the sub-problems is reached, the end error is not lower than the threshold value, and the rule is failed. And recording the planning success rate and the average calculation time when the planning is successful.
The success rate and calculation time of Monte Carlo simulation planning are shown in Table 5. Because the initial value fluctuation range is large, part of the random initial values may not be feasible, and because the planning of nonlinear aerodynamic force is considered to be a non-convex problem, part of the initial value planning difficulty is large, and in some algorithms, the solution meeting the precision requirement is difficult to converge under the limit of practical feasible iteration steps. From the results, the end error method is calculated more efficiently than the acceleration error method (FSOCP) at cold start, but the planning success rate is slightly lower. After the hot start is used, the programming success rate and the calculation efficiency of the tail end error method are higher than those of the acceleration error method, and when each sub-problem is solved for 1 step, the calculation cost is only 10.7% of that of the acceleration error method (FSOCP). In addition, the calculation efficiency and the solving success rate of the acceleration error method are higher than those of ECOS by using FSOCP.
Table 5 Monte Carlo simulation plan success rate and calculation time contrast
The result verifies that the end error method has higher calculation efficiency than the acceleration error method, has the capability of pressing the end position error in the specific direction by the heavy point, and can obtain higher solving success rate than the acceleration error method through hot start.
Those skilled in the art will appreciate that the above-described modifications may be implemented by those skilled in the art in combination with the prior art and the above-described embodiments, and are not described herein. Such modifications do not affect the essential content of the present invention, and are not described herein.
The preferred embodiments of the present invention have been described above. It is to be understood that the invention is not limited to the specific embodiments described above, wherein devices and structures not described in detail are to be understood as being implemented in a manner common in the art; any person skilled in the art will make many possible variations and modifications, or adaptations to equivalent embodiments without departing from the technical solution of the present invention, which do not affect the essential content of the present invention. Therefore, any simple modification, equivalent variation and modification of the above embodiments according to the technical substance of the present invention still fall within the scope of the technical solution of the present invention.

Claims (3)

1. A rocket stage recovery landing zone power descent guidance method based on terminal errors is characterized by comprising the following steps of
Step 101: inputting initial total flight time t f, discrete time step number k f, sub-problem number upper limit n SC, time step change trust zone upper limit eta Δt, thrust change trust zone upper limit eta T and trust zone adjustment coefficient beta;
Step 102: initializing;
Step 103: if i=1, then SOCP problem constraints are generated, in which case either no trust zone constraints are used, or a larger trust zone boundary is used; if i > 1, updating SOCP the problem constraint;
Step 104: solving SOCP problems; calculating the position and speed error of the tail end through fine grid numerical simulation;
Step 105: calculating an improvement ratio ζ= (J L0,i-JL0,i-1)/(JL1,i-JL1,i-1); if ζ is greater than or equal to ζ max, if a trusted region boundary is activated, multiplying the activated boundary by β, wherein the radius of the activated boundary corresponds to the trusted region radius η Δt or η T; if ζ is less than or equal to ζ min, dividing the radius of the trust zone η Δt,ηT by β; if ζ is less than or equal to 0, rejecting SOCP the problem, and resetting to the solution of the last sub-problem, i.e mi[k]＝mi-1[k],Γi[k]＝Γi-1[k],ri[k]＝ri-1[k],vi[k]＝vi-1[k],ai[k]＝ai-1[k],aR,i[k]＝aR,i-1[k],k∈{0,1,L,kf},Δti＝Δti-1;
Step 106: updating the total flight time t f;
step 107: if the end position and speed error is smaller than the preset limit, step 109 is executed;
Step 108: if i is less than n SC, i=i+1, repeating steps 103 to 106; if i=n SC, then step 109 is performed;
step 109: outputting total flight time T f, mass m, position r, speed v and thrust T;
Wherein, Is the objective function value of the plan; j L1＝-m(kf)+ωκr||r[kf]||+ωκv||v[kf || is the objective function value of the simulation; /(I)The mass, the position and the speed are calculated through numerical simulation, and m, r and v are the mass, the position and the speed in SOCP solving results; i is a sub-problem sequence number;
The initialization in step 102 is specifically:
2. A rocket sub-level recovery landing zone power descent guidance method based on end error as claimed in claim 1, wherein hot start can be supported, acceleration is performed using correlation between SOCP problems; when the hot start is used, the method also comprises the step of outputting the initial value of the current SOCP problem (x 0,y0,s0) by a SOCP problem hot start initial value correction method before the 'solution SOCP problem';
The 'SOCP problem hot start initial value correction method' comprises the following steps:
step 201: solution of input existing early SOCP sub-problem The current sub-problem equation constrains the coefficient matrix A, the right-end term b, the cone constraint dimension (l, S 1,S2,L,Sm), the correction coefficient η 0;
Step 202: initializing, η=max (1/(|a| ∞+||b||∞),η0);
step 203: initializing, i=1;
Step 204: i+＝Sj，/>
Step 205, if i is less than or equal to m, repeating step 204; if i > m, go to step 206;
step 206: outputting an initial value (x 0,y0,s0) of the current SOCP questions;
Wherein, the default value of the correction coefficient eta 0 is 0.001.
3. The rocket sublevel recovery landing zone power descent guidance method based on end error of claim 2, further comprising outputting an initial value of the current SOCP problem (x 0,y0,s0) by a SOCP problem hot start initial value correction method before solving SOCP problems; step 105 is omitted.
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