CN119717512B

CN119717512B - Uncertainty quantification-based detector power drop robust optimal guidance method

Info

Publication number: CN119717512B
Application number: CN202411819832.6A
Authority: CN
Inventors: 龚有敏; 肖以正; 梅杰; 马广富
Original assignee: Harbin Institute Of Technology shenzhen Shenzhen Institute Of Science And Technology Innovation Harbin Institute Of Technology
Current assignee: Harbin Institute Of Technology shenzhen Shenzhen Institute Of Science And Technology Innovation Harbin Institute Of Technology
Priority date: 2024-12-11
Filing date: 2024-12-11
Publication date: 2025-09-16
Anticipated expiration: 2044-12-11
Also published as: CN119717512A

Abstract

The invention relates to an uncertainty quantification-based robust optimal guidance method for power drop of a detector. The method comprises the steps of constructing a power-down robust fuel optimal guidance model considering initial state and model environment uncertainty, converting the optimal guidance model into a deterministic problem through an uncertainty quantization method based on chaotic polynomial expansion, and solving the deterministic optimization problem through a sequence convex optimization method to obtain a robust optimal landing track and a corresponding feedback guidance law. The invention can convert the complex nonlinear optimal control problem containing randomness into the convex optimization problem which is easy to solve, improves the solving efficiency on the premise of ensuring the solving success rate, can meet various constraints under the uncertain condition of the designed optimal track, and can be directly applied on line by the obtained corresponding feedback guidance law.

Description

Uncertainty quantification-based detector power drop robust optimal guidance method

Technical Field

The invention relates to an uncertainty quantification-based robust optimal guidance method for power drop of a detector, and belongs to the technical field of power drop control of detectors.

Background

Along with the enhancement of the onboard computing capability of the detector and the gradual maturity of the technology of the linear track planning represented by convex optimization, the optimal guidance becomes the development trend of the future Mars power descent guidance technology, and has the following main characteristics that 1, a numerical algorithm is used for replacing a guidance law of a fixed structure, the generation of guidance instructions highly depends on a large number of onboard computing, 2, the guidance instructions are generated based on models or data, a specific reference track and a large number of offline designs are not needed, and 3, the optimality is pursued. The above three features enable optimal guidance to ensure target optimality (often manifested as fuel optimality in the detector power down segment) while ensuring satisfaction of various constraints, an advantage that is not comparable to conventional explicit guidance laws. Many existing studies on optimal guidance have focused mainly on fast trajectory optimization algorithms and corresponding guidance law generation.

During a power down landing, the probe is often subject to various uncertainties, such as system initial state uncertainty, system parameter uncertainty, and the like. In order to achieve high-precision and high-safety landing, the influence of the uncertainty on the track is necessarily included in the design of the guidance law, namely, a robust optimal guidance problem considering the uncertainty is constructed. However, in the robust optimal guidance problem, the system dynamics, problem constraints and even objective functions are often random, so that the robust optimal guidance problem becomes a random optimal control problem, which cannot be directly solved according to the existing method, and therefore, the random functions need to be converted into deterministic functions. Uncertainty quantification is an effective means for quantitatively describing and evaluating uncertainty and evolution thereof in a system, and mainly comprises two parts of uncertainty characterization and uncertainty propagation, wherein the uncertainty characterization is a process of establishing a mathematical model according to data of uncertainty variables, and the uncertainty propagation is a propagation condition of random states of a research system along with system dynamics under the condition that the uncertainty exists. The uncertainty quantization mode of the system can be mainly divided into linear and nonlinear modes, wherein the linear covariance propagation method utilizes the propagation rule of the linear system to analyze the evolution of the mean value and covariance of the system, however, for nonlinear systems such as Mars power reduction, the accuracy of the linear method is often limited.

Disclosure of Invention

The invention provides an uncertainty quantification-based detector power drop robust optimal guidance method, which aims to at least solve one of the technical problems in the prior art.

The technical scheme of the invention relates to an uncertainty quantification-based detector power drop robust optimal guidance method, which comprises the following steps:

S100, constructing a power-down robust fuel optimal guidance model considering initial state and model environment uncertainty;

s200, converting the optimal guidance model into a deterministic problem through an uncertainty quantization method based on chaotic polynomial expansion;

And S300, solving a deterministic optimization problem through a sequence convex optimization method to obtain a robust optimal landing track and a corresponding feedback guidance law.

Further, for the step S100,

In the power-down robust fuel optimal guidance model, the objective function of the optimization problem is expressed as follows:

constraints for its optimization problem include:

a spark detector dynamics system under uncertainty conditions, expressed as follows:

constraints for limiting the thrust amplitude high probability to be in a given range are expressed as follows:

constraints for ensuring that the detector does not collide with the ground with a high probability are expressed as follows:

μ(r_z(t;ξ))-εσ(r_z(t;ξ))≥0

the initial conditions and terminal conditions of the optimization problem are expressed as follows:

m(t₀)＝m₀(ξ)

Wherein l epsilon { x, y, z } represents a certain dimension in the three-dimensional space, r _l (t; ζ) and v _l (t; ζ) respectively represent the position and the speed of the detector in the l direction under the influence of the randomness of the system; respectively representing a given terminal position and a terminal speed expectation; Respectively representing standard deviation upper bounds of a given terminal position and terminal speed, m (t; xi) representing detector mass, r _l0(ξ),v_l0(ξ),m₀ (xi) respectively representing initial position, speed and mass of the detector, t _f representing given terminal time, g representing a Mars gravity acceleration vector, and alpha (xi) representing thruster parameters; Is the thrust vector of the thruster, ρ ₁,ρ₂ represents the lower and upper bounds of the thrust bipartite respectively, ε is a constant for measuring the robustness, and a larger ε value means a smaller probability of constraint breaking.

Further, in the step S100,

Thrust vectorIs divided into a nominal thrust part and a state feedback part, it is represented as follows

In the formula,As a deterministic nominal thrust vector,Designed as a linear feedback control amount with respect to μ (r _l(t_f; ζ)) and μ (v _l(t_f; ζ)), wherein,

Where K _rl,K_vl is the feedback gain for the position and velocity errors in the i-direction, respectively.

Further, in the step S200:

The invasive chaotic polynomial expansion method is adopted, and is expressed as follows:

where <, > represents the inner product in Hilbert space extended by the base { Φ _j }, i.e

<f(ξ)g(ξ)>=∫f(ξ)g(ξ)W(ξ)dξ

Where W (ζ) represents the corresponding weight function selected from the probability density function of the uncertainty source ζ.

Further, in the step S200:

carrying out random dynamics uncertainty quantification based on a chaotic polynomial expansion method on a Mars detector dynamics system under the uncertainty condition to obtain an objective function deterministic form of a power-down robust fuel optimal guidance model;

The deterministic system obtained after the uncertainty of the power-down robust fuel optimal guidance model is quantized is expressed as follows:

Wherein, the vectors containing all the corresponding chaos polynomial coefficients are respectively expressed as follows:

wherein R, V and M respectively represent high-dimensional polynomial coefficient vectors obtained by expanding the chaotic polynomials of the position, the speed and the quality of the detector; representing vectors formed by all state quantities in a deterministic system obtained after uncertainty quantization; a vector representing the system control amount; for introduction of Substitute variable, satisfy

Further, in the step S300:

the construction method based on the convex programming problem uses discretization and linearization to carry out the convex on the system dynamics, the problem constraint and the objective function, and adds the trust domain constraint and the virtual control constraint so as to solve by utilizing the sequence convex optimization technology.

Further, in the step S300:

The sequence convex optimization method comprises the following steps:

Taylor expansion of deterministic system dynamics (10) at reference system state and control quantity X ^*(t),U^* (t) yields a linearized dynamics system, which is represented as follows:

In the formula, A linearized system state matrix and a linearized control matrix;

And dispersing the obtained linear dynamics system by using an Euler method, wherein the discrete time interval of the Euler method is delta t, so that the obtained linear dynamics system is obtained:

And then can obtain:

In the formula,

The values of the system state/control matrix, the system state/control quantity and the system reference state/control quantity at discrete time points t _k are respectively represented.

Further, in the step S300:

the power-down robust fuel optimal guidance model is constructed as a convex programming problem, which is expressed as follows:

constraints for its optimization problem include:

the resulting kinetic constraints after the salifying of the deterministic system of the dynamic descent robust fuel-optimized guidance model are expressed as follows:

In the formula, Respectively representing a state matrix and a control matrix obtained after the high-dimensional system is developed by the chaos polynomial and the linearization of the high-dimensional system; V _k denotes a virtual control amount;

A convex constraint comprising a linear equality constraint or a second order cone inequality constraint, expressed as follows:

for alternative variable relation The linear expansion can be obtained:

constraint of the difference delta between the optimization state and the control quantity of two adjacent rounds is expressed as follows:

wherein K is the total length of the discrete time domain; A linearized system state matrix and a control matrix, respectively.

The invention also relates to a computer readable storage medium having stored thereon program instructions which, when executed by a processor, implement the above-mentioned method.

The technical scheme of the invention also relates to a robust optimal guidance method for the power drop of the detector from the encoder and the graph annotation force network, and the system comprises a computer device which comprises the computer readable storage medium.

The beneficial effects of the invention are as follows:

Aiming at the problem of Mars power descent, the invention provides robust optimal guidance based on an uncertainty quantification technology, an optimal guidance model considering the initial state and the model environment uncertainty is constructed, the optimal guidance model is converted into a deterministic problem by using an uncertainty quantification method based on chaotic polynomial expansion, and the solution of the deterministic optimization problem is carried out by a sequence convex optimization method, so that a robust optimal landing track and a corresponding feedback guidance law are obtained. The invention can convert the complex nonlinear optimal control problem containing randomness into the convex optimization problem which is easy to solve, and improves the solving efficiency on the premise of ensuring the solving success rate. The invention can design the optimal track and take uncertainty of the model and the environment into consideration, so that the designed optimal track can meet various constraints under the uncertainty condition. The method and the device have the advantages that the corresponding feedback guidance law is obtained while the track is optimized, the feedback guidance law can be directly applied on line, and the on-line calculation load is reduced.

Drawings

Fig. 1 is a basic flow chart of the method according to the invention.

Fig. 2 is a schematic diagram of detector track spread according to the method of the present invention.

Fig. 3 is a schematic representation of the triaxial thrust force of the probe according to the method of the present invention over time.

Fig. 4 is a graph showing the thrust second norm of the detector according to the method of the present invention over time.

Fig. 5 is a schematic diagram of the change in detector state over time according to the method of the present invention.

Fig. 6 is a schematic view of the falling point spread of the detector according to the method of the invention.

Detailed Description

The conception, specific structure, and technical effects produced by the present invention will be clearly and completely described below with reference to the embodiments and the drawings to fully understand the objects, aspects, and effects of the present invention.

It should be noted that, unless otherwise specified, when a feature is referred to as being "fixed" or "connected" to another feature, it may be directly or indirectly fixed or connected to the other feature. As used herein, the singular forms "a", "an" and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise. Furthermore, unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art. The terminology used in the description presented herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. The term "and/or" as used herein includes any combination of one or more of the associated listed items.

It should be understood that although the terms first, second, third, etc. may be used in this disclosure to describe various elements, these elements should not be limited by these terms. These terms are only used to distinguish one element of the same type from another. For example, a first element could also be termed a second element, and, similarly, a second element could also be termed a first element, without departing from the scope of the present disclosure. The use of any and all examples, or exemplary language (e.g., "such as") provided herein, is intended merely to better illuminate embodiments of the invention and does not pose a limitation on the scope of the invention unless otherwise claimed.

Referring to fig. 1 to 4, in some embodiments, the robust optimal guidance method for detector power dip based on uncertainty quantization according to the present invention comprises at least the following steps:

S200, converting an optimal guidance model into a deterministic problem through an uncertainty quantization method based on chaotic polynomial expansion;

In some embodiments, the invention provides a robust optimal guidance scheme based on uncertainty quantization technology aiming at the problem of Mars power reduction, which firstly builds an optimal guidance problem considering initial state and model environment uncertainty. Specifically, a generally nonlinear system with system initial state and parameter uncertainty:

In the formula, State vectors representing the system and initial values containing uncertainty, respectively; representing a system parameter vector containing uncertainty; representing a system control input containing uncertainty. The initial state and parameter uncertainties are caused by different sources of uncertainty, denoted as At the same time, the uncertainty sources each satisfy their corresponding probability distribution.

Further, x ₀ (ζ), u (ζ) and a (ζ) may be expressed as relative to the respective nominal valuesA ⁿ,uⁿ function with uncertainty source ζ:

In some embodiments, the present invention converts the optimal guidance model into a deterministic problem by an uncertainty quantization method based on a chaotic polynomial expansion.

Specifically, according to the chaos polynomial theory, the random variables x (ζ), u (ζ), a (ζ) may each be represented by a corresponding chaos polynomial expansion model. Further, for computational reasons, it is often of a certain orderTruncation, where p is the order selected for a single uncertainty source, as shown in equations (5) through (7):

In the formula, The j-th order chaotic polynomial coefficient representing a random variable (·) _i, Φ (ζ) is an orthogonal polynomial basis selected according to the form of an uncertainty source ζ, the random distribution of which is selected as a standard random distribution satisfying the Askey scheme.

By the expansion of the chaotic polynomials of the formulas (5) to (7), deterministic time-varying chaotic polynomial coefficientsAnd (3) withThe method is decoupled from an orthogonal polynomial basis phi (xi) containing the random characteristic of the system, and the xi is eliminated through a proper mathematical method, so that the original random differential equation (1) can be solved.

Further, the patent adopts an invasive chaotic polynomial expansion method, brings the formulas (5) to (7) into the formula (1) and simultaneously projects two sides of the equation to phi (xi) to obtain

In formula (8), < ·, · > represents the inner product in Hilbert space extended by the base { Φ _j }, i.e

Further, table 1 gives the basis functions of the optimal orthogonal polynomials corresponding to the common distribution types. It will be appreciated that the probability density function corresponding to the same distribution type is similar to the weight function form, ensuring that the orthogonal polynomial bases are optimal with respect to a certain probability distribution type.

TABLE 1 orthogonal polynomials corresponding to different random variables

On the right side of equation (8), the term < Φ _l ² (ζ) > in the denominator can be resolved according to the inner product definition equation (9), however, for the molecular term, due to the nonlinearity of the system dynamics, the integral term is difficult to resolve, and a numerical integration method, such as a full factor numerical integration method, is often required.

In the present invention, equation (8) converts a random system originally comprising n random states into a deterministic system comprising n _s =n·p 'states, where P' =p+1:

wherein X, U, a represent all polynomial coefficients used to construct the chaotic polynomial expansion of X, U, a, respectively:

The deterministic system described by the formula (10) forms a proxy model of the original random system (1), and the state of the deterministic system can be efficiently obtained by using a system evolution method such as an Euler method, a fourth-order Dragon-Kutta method and the like. Further, to describe the state statistical properties of the random system (1), the statistical moment of states such as the mean μ (X _i) and the variance σ (X _i) can be analytically found using the chaos polynomial coefficient X:

where E [. Cndot ] represents the expected value of the corresponding random variable.

In an application embodiment, the method and the device can be applied to the problem of robust optimal guidance, and it can be understood that the main purpose of the problem of robust optimal guidance is to quantify the scattering condition of the track by using statistical moments (such as mean value, variance and the like), and plan out a corresponding minimum fuel consumption thrust sequence so as to ensure that the track generated under the thrust sequence can still ensure the satisfaction of constraint under the uncertain condition. Specifically, in the power-down robust fuel optimal guidance model, the objective function of the optimization problem is expressed as follows:

Subject to the following conditions (constraint on the optimization problem):

μ(r_z(t;ξ))-εσ(r_z(t;ξ))≥0 (22)

m(t₀)＝m₀(ξ) (25)

It will be appreciated that equation (16) above is an objective function of the optimization problem, and equations (17) through (25) are constraints of the optimization problem. Wherein, the formulas (17) to (19) represent the dynamics of the Mars detector under the condition of uncertainty, the formulas (20) and (21) limit the thrust amplitude to be in a given range with high probability, thereby ensuring that the detector can realize a desired track, the formula (22) ensures that the detector does not collide with the ground with high probability, thereby ensuring the safety of the detector under the condition of uncertainty, and the formulas (23) to (25) give the initial condition and the terminal condition of the optimization problem.

Further, thrust vectorCan be decomposed into a nominal thrust and a state feedback, namely

In some embodiments, the power-down robust fuel optimal guidance problem is a nonlinear programming problem containing random variables, and in order to solve the optimization problem, the invention firstly converts the problem into a deterministic problem by using an uncertainty quantization method based on chaotic polynomial expansion. Further, to improve the efficiency of the solution of the resulting deterministic nonlinear programming problem, it can be constructed as a convex programming problem. The convex programming problem requires that both the objective function and the constraint of the system be convex functions.

Specifically, first, taylor expansion is performed on deterministic system dynamics (10) at reference system state and control quantity X ^*(t),U^* (t), resulting in a linearized dynamics system:

In the formula, Is a linearized system state matrix and a control matrix.

Further, the obtained linear system (28) is discretized by using the Euler method, and the discrete time interval thereof is Δt, and then:

finishing formula (29), obtaining:

In the formula,

Detailed description of steps S100 and S200

In the model construction and uncertainty quantification of the robust guidance problem, the optimal guidance model of the power-down robust fuel taking the initial state and the uncertainty of the system parameters into consideration is constructed according to the optimal guidance problem of the power-down robust fuel shown in the formulas (16) to (25). In order to solve the optimal guidance problem of the power-down robust fuel, the invention adopts an uncertainty quantization method based on a chaos polynomial to carry out deterministic transformation on random variables containing uncertainty in the optimal guidance problem of the power-down robust fuel, and the method specifically comprises random dynamics, problem constraint and uncertainty quantization of an objective function.

Specifically, the random dynamics uncertainty quantization based on the chaotic polynomial expansion method shown in the formula (8) is carried out on the random dynamics formulas (17) to (19) of the system, and the result is that:

Because of the presence of the uncertainty thrust double norm in the molecule to the right of equation (33), the inner product term in the molecule is very difficult to solve, thus introducing a surrogate variable And satisfies the corresponding equality constraint:

uncertainty quantization of the formula (34) as shown in the formula (8) is performed to obtain:

Using the random variable statistical moment solving methods described by the formulas (14) and (15) to the formulas (20) to (25), it is obtained that:

the objective function in the power-down robust fuel-optimized guidance model, equation (16), may be rewritten as a deterministic form as follows:

Wherein, the

Each vector containing all of the corresponding chaotic polynomial coefficients. For simplicity, the deterministic system obtained after uncertainty quantization is noted as:

In the formula, a represents a polynomial coefficient vector obtained by expanding an uncertain parameter a by a chaotic polynomial, and t represents time.

Detailed description of step S300

The invention discloses a construction method based on convex programming problem, which uses discretization and linearization to carry out the convex on system dynamics, problem constraint and objective function, and adds trust domain constraint and virtual control constraint so as to solve by utilizing a sequence convex optimization technology.

In particular, the power-down robust fuel optimal guided projection planning problem,

Subject to the following conditions (constraint on the optimization problem):

wherein K is the total length of the discrete time domain; is a linearized system state matrix and a control matrix.

The expression (51) is a dynamic constraint obtained by subjecting the expression (49) to the method shown in the expression (30), the expression (58) is a linear expansion of the substitution variable relation (35), and the expressions (52) to (57) include a series of linear equality constraints or second order cone inequality constraints, which are both convex constraints, so that no additional projection processing is required. In order to prevent the problem of 'artificial infeasibility' caused by local linearization dynamics, a virtual control quantity V _k is added in the formula (51), and meanwhile, in order to reduce errors caused by linearization, the formula (59) constrains the difference between the optimized states and the control quantity of two adjacent rounds, which is represented by delta. Finally, V _k, Δ and their corresponding weights w _V,w_Δ are added to the objective function.

The method solves the problem of robust guidance through a sequence convex optimization method. The sequential convex optimization method approximates the solution of the original problem by continuously solving the convex problem obtained by expanding at the current reference state, and the flow is shown in the algorithm 1:

the present invention is herein, in one embodiment, simulated verification.

Specifically, simulation and optimization algorithm parameters are shown in the table:

TABLE 2 Mars environment and detector related parameter values

Assuming that the thruster coefficient α, the initial position r ₀ has uncertainty, specific uncertainty information and corresponding PCE are shown in table 3:

TABLE 3 uncertainty in kinetic systems

The simulation hardware platform is as follows, CPU is AMD R7-5800H (8 core 16 threads), main frequency is 2.5GHz, and running memory is 32GB. The convex optimization problem is solved using MOSEK solver.

The validity of the invention is verified. Firstly, a robust optimal guidance problem is constructed according to the table 2 and the table 3, and a sequence convex optimization technology is utilized for solving. And constructing a feedback guidance law by using the solved linear feedback gain K _rl(t),K_vl (T) and the nominal thrust T _l (T). Next Monte Carlo simulation was performed, generating 2000 sets of samples using the uncertainties present in the dynamics system given in Table 2, and landing guidance was performed using the resulting feedback guidance law.

Wherein fig. 2 shows the scattering situation of the track, it can be seen that under the action of the designed robust optimal feedback guidance law, the detector can realize soft landing under the condition that the initial state uncertainty and the parameter uncertainty exist. Wherein, figures 3 and 4 show the triaxial thrust and thrust norm of the probe under uncertain conditions, respectively. It can be seen that the designed robust optimal feedback guidance law ensures that the thrust norms are within a given interval, even if affected by uncertainty. Furthermore, the resulting thrust norms still have the form bang-bang, similar to the deterministic optimal thrust case.

To further clarify the effectiveness of the designed robust optimal feedback guidance law, fig. 5 shows a plot of detector position versus velocity over time. It can be seen that the z-axis height of the detector is always greater than zero, and the proposed algorithm can ensure the safety of the detector in the case of uncertainty. Fig. 6 shows a scatter plot of the drop points, it can be seen that in most cases the drop points of the detector are constrained to be within a preset μ±3σ range (in the color ellipsoid of fig. 6).

It should be noted that most of the research on optimal guidance in recent years only focuses on the problem of deterministic track planning, that is, the influence of model and environmental uncertainty and external disturbance on the track is not considered in track planning, so that only a nominal track which meets constraint under deterministic condition and has optimality can be obtained. Although, under the conventional "track planning-track tracking" guidance scheme, cancellation of disturbance and uncertainty can be achieved by designing a robust tracking controller that outputs a nominal track guidance command online without placing in a track planning link, these tracking controllers can be broadly divided into two types, i.e., an active compensation controller based on feedforward and a passive compensation controller based on feedback, according to the design principle thereof. However, whichever tracking controller is adopted, the tracking controller and the optimal track under the scheme are independently designed, and the optimal track cannot consider the output of the tracking controller, which inevitably leads to the influence of the optimality of the actual track.

It should be appreciated that the method steps in embodiments of the present invention may be implemented or carried out by computer hardware, a combination of hardware and software, or by computer instructions stored in non-transitory computer-readable memory. The method may use standard programming techniques. Each program may be implemented in a high level procedural or object oriented programming language to communicate with a computer system. However, the program(s) can be implemented in assembly or machine language, if desired. In any case, the language may be a compiled or interpreted language. Furthermore, the program can be run on a programmed application specific integrated circuit for this purpose.

Furthermore, the operations of the processes described herein may be performed in any suitable order unless otherwise indicated herein or otherwise clearly contradicted by context. The processes (or variations and/or combinations thereof) described herein may be performed under control of one or more computer systems configured with executable instructions, and may be implemented as code (e.g., executable instructions, one or more computer programs, or one or more applications), by hardware, or combinations thereof, collectively executing on one or more processors. The computer program includes a plurality of instructions executable by one or more processors.

Further, the method may be implemented in any type of computing platform operatively connected to a suitable computing platform, including, but not limited to, a personal computer, mini-computer, mainframe, workstation, network or distributed computing environment, separate or integrated computer platform, or in communication with a charged particle tool or other imaging device, and so forth. Aspects of the invention may be implemented in machine-readable code stored on a non-transitory storage medium or device, whether removable or integrated into a computing platform, such as a hard disk, an optical read and/or write storage medium, RSM, ROM, etc., such that it is readable by a programmable computer, which when read by a computer, is operable to configure and operate the computer to perform the processes described herein. Further, the machine readable code, or portions thereof, may be transmitted over a wired or wireless network. When such media includes instructions or programs that, in conjunction with a microprocessor or other data processor, implement the steps described above, the invention described herein includes these and other different types of non-transitory computer-readable storage media. The invention may also include the computer itself when programmed according to the methods and techniques of the present invention.

The computer program can be applied to the input data to perform the functions described herein, thereby converting the input data to generate output data that is stored to the non-volatile memory. The output information may also be applied to one or more output devices such as a display. In a preferred embodiment of the invention, the transformed data represents physical and tangible objects, including specific visual depictions of physical and tangible objects produced on a display.

The present invention is not limited to the above embodiments, but can be modified, equivalent, improved, etc. by the same means to achieve the technical effects of the present invention, which are included in the spirit and principle of the present invention. Various modifications and variations are possible in the technical solution and/or in the embodiments within the scope of the invention.

Claims

1. A robust optimal guidance method for probe power descent based on uncertainty quantification, characterized in that the method comprises the following steps:

S100, construct a robust fuel optimal guidance model for powered descent that takes into account the uncertainty of the initial state and model environment;

S200, converting the optimal guidance model into a deterministic problem through an uncertainty quantification method based on chaotic polynomial expansion;

S300, solving a deterministic optimization problem using a sequential convex optimization method to obtain a robust optimal landing trajectory and a corresponding feedback guidance law;

Wherein, for the step S100,

In the powered descent robust fuel optimal guidance model, the objective function of the optimization problem is expressed as follows:

The constraints of the optimization problem include:

The dynamic system of the Mars rover under uncertainty is expressed as follows:

The constraint used to limit the thrust amplitude to a given range is expressed as follows:

The constraints used to ensure that the probe does not collide with the ground are expressed as follows:

μ(r _z (t；ξ))-εσ(r _z (t；ξ))≥0

The initial and terminal conditions of the optimization problem are expressed as follows:

m(t ₀ )＝m ₀ (ξ)

Where l∈{x,y,z} represents a dimension in three-dimensional space; r _l (t;ξ) and v _l (t;ξ) represent the position and velocity of the detector in the l direction under the influence of system randomness, respectively. Represent the given terminal position and terminal velocity expectations respectively; Respectively represent the upper bounds of the standard deviation of the given terminal position and terminal velocity; m(t;ξ) represents the mass of the probe; r _l0 (ξ), v _l0 (ξ), m ₀ (ξ) represent the initial position, velocity and mass of the probe, respectively; t _f represents the given terminal time; g represents the Martian gravity acceleration vector; α(ξ) represents the thruster parameters; is the thrust vector of the thruster; ρ ₁ ,ρ ₂ represent the lower and upper bounds of the thrust norm, respectively; ε is a constant used to measure robustness; a larger ε value means a smaller probability of the constraint being broken.

2. The method according to claim 1, characterized in that in step S100,

thrust vector It is decomposed into two parts: nominal thrust and state feedback, which are expressed as follows

Where, is the deterministic nominal thrust vector, It is designed as a linear feedback control quantity about μ(r _l (t _f ; ξ)) and μ(v _l (t _f ; ξ)), where

Where K _rl and K _vl are the feedback gains of position and velocity errors in direction l, respectively.

3. The method according to claim 1, wherein in step S200:

The intrusive chaotic polynomial expansion method used is expressed as follows:

Where <·,·> represents the inner product in the Hilbert space expanded by the basis {Φ _j }, that is,

<f(ξ)g(ξ)>＝∫f(ξ)g(ξ)W(ξ)dξ

Where W(ξ) represents the corresponding weight function selected according to the probability density function of the uncertainty source ξ.

4. The method according to claim 3, characterized in that in step S200:

The stochastic dynamic uncertainty of the Mars rover dynamic system under uncertainty is quantified based on the chaotic polynomial expansion method, and the deterministic form of the objective function of the robust fuel optimal guidance model for powered descent is obtained;

The deterministic system obtained after uncertainty quantification of the robust fuel optimal guidance model for powered descent is expressed as follows:

Among them, the vectors containing all corresponding chaotic polynomial coefficients are expressed as follows:

Where R, V, and M represent the high-dimensional polynomial coefficient vectors obtained by expanding the position, velocity, and mass of the detector through chaotic polynomials, respectively. Represents the vector consisting of all state quantities in the deterministic system obtained after uncertainty quantification; Represents the vector composed of the system control quantity; For the introduction Substitution variables satisfy

5. The method according to claim 4, characterized in that in step S300:

Based on the construction method of convex programming problem, discretization and linearization are used to convexify the system dynamics, problem constraints and objective function, and trust region constraints and virtual control constraints are added to facilitate the solution using sequential convex optimization technology.

6. The method according to claim 5, characterized in that in step S300:

The sequential convex optimization method comprises:

Taylor expansion of the deterministic system dynamics (10) at the reference system state and control variables X ^* (t), U ^* (t) yields a linearized dynamic system, which is expressed as follows:

Where, is the linearized system state matrix and control matrix;

The obtained linearized dynamic system is discretized using the Euler method, with the discrete time interval Δt being Δt, to obtain:

Then we get:

Where,

X _k =X(t _k ),U _k =U(t _k ), point

They represent the values of the system state/control matrix, system state/control quantity and system reference state/control quantity at the discrete time point _tk .

7. The method according to claim 6, characterized in that in step S300:

The robust fuel optimal guidance model for powered descent is formulated as a convex programming problem, which is expressed as follows:

The constraints of the optimization problem include:

The dynamic constraints obtained by convexifying the deterministic system of the robust fuel optimal guidance model for powered descent are expressed as follows:

Where, They represent the state matrix and control matrix of the high-dimensional system after the chaotic polynomial expansion and its linearization, respectively; _Vk represents the virtual control quantity;

Convex constraints, including linear equality constraints or second-order cone inequality constraints, are expressed as follows:

For substitution variables Performing linear expansion yields:

The constraint of the difference Δ between the optimization state and the control quantity in two adjacent rounds is expressed as follows:

Where K is the total length of the discrete time domain; are the linearized system state matrix and control matrix respectively.

8 . A computer-readable storage medium having program instructions stored thereon, wherein the program instructions are configured to implement the method according to claim 1 when executed by a processor.

9. A robust optimal guidance method for detector power descent, characterized by comprising:

A computer device comprising the computer-readable storage medium according to claim 8.